Hi Elise,
Lets first take a look at each of your criteria so that it becomes easier to see which material meets each criteria since there will be some tradeoffs involved in your decisions. Taken as a whole … and to the extreme … your criteria have pretty much eliminated every mattress in existence 
- If your mattress contains any foam … then memory foam is the hottest, polyfoam is next, and latex is the coolest.
- Some foam contains “cooling materials” which can change their heat characteristics such as gels in memory foam or “phase change” materials in latex (like Celsion) but the “order of coolness” is still the same.
- How deep you sink into the upper layers of a mattress also affects heat … the deeper the hotter but the tradeoff here is that you may find less pressure relief if you don’t sink in deep enough.
-Natural fibers and no foam in a mattress tend to be the coolest of all … like the “old fashioned mattresses” made of cotton, wool, and horsehair on top of innersprings.
- Mattress ticking and quilting will also affect heat and some of the newer temperature regulating materials can lessen heat as well … as can natural fibers used in the ticking and quilting.
The “edge” here goes to the “old fashioned innerspring” mattresses without any foam at all followed by latex comfort layers with natural and more breathable fibers in the ticking and quilting or temperature regulating tickings.
Your bedding such as mattress pads and the sheets and blankets you use can also make a big difference here.
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In the comfort layers, memory foam is the least motion transferring closely followed by latex foam and then followed by polyfoam. Natural fibers are the most motion transferring … especially because they are almost always over innersprings.
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In the support layers (where memory foam cannot be used because it is too soft) … latex foam is the least motion transferring followed by polyfoam followed by innersprings. Of the innersprings, pocket or marshall coils are the least motion transferring followed by various types of offset coils however the method of construction of innersprings will also play a part here. Smaller movements are mostly absorbed by the upper layers of a mattress while larger movements are affected by both the upper layers and the lower layers.
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The firmness and density of any foam used in a mattress will also play a role in how motion isolating it will be.
The edge here goes to memory foam or latex comfort layers over latex, HD polyfoam, or pocket coils.
Higher density slower recovery memory foams are the worst here … followed by lower density faster recovery memory foams. These are really the only two types of foam where resiliency (foam rebound and energy absorbtion) is exceptionally low. Polyfoam doesn’t absorb nearly as much energy as memory foam while latex is the most resilient foam of all. Natural fibers have differing levels of resiliency depending on how they are tufted and constructed with animal hair in general being the most resilient (horse hair and pig hair are more resilient than wool with cotton being among the least). In general though … animal fibers are less resilient than high quality foam. The only real issues from a “sleeping in mud” feeling is with memory foam, particularly the higher density and slower recovery versions.
The edge here goes to anything except memory foam or low resilience natural fibers that develop too deep a “body shape” over time.
Free movement while sleeping is a combination of the resilience of a material and how deeply you sink into a material. In general … this would exclude memory foams which is the material with the lowest resilience and at the same time forms the deepest pressure relieving cradle.
There are different types of offgassing and smells associated with different materials. Even feathers or wool of some types can have a bad smell when new even though this is not the “offgassing” of various chemicals. Natural latex has a rubbery smell when its new and blended latex sometimes has a vanilla smell from an additive that is included. Memory foam is the most “famous” for offgassing (smell that comes from volatile organic compounds and chemicals that are not “natural”) however most of the quality foams have been tested for VOC emissions and are considered “safe”. Innersprings are really the only material that has no smell connected to it while natural fibers typically have less than foams.
CertiPur tests the foams they certify and an even more stringent testing is done by Oekotex Class 1. Depending on how long the memory foam has aired out however and also depending on the sensitivity of the individual … some people may still be sensitive to the “smells” that come from memory foam even though it has been tested. All materials can have a smell associated with them and in most cases … the more natural materials that have a “smell” are not as harmful than the synthetic materials that have a more “chemical” smell attached to them. Of the foams, and speaking only in generic terms, … latex (especially 100% natural latex) is “healthier” than polyfoam which is mostly petrochemical based which is in turn “less harmful” than memory foam which is polyfoam with even more chemicals added to it. This is a subject of some debate with many conflicting opinions about the levels of various types of “offgassing” that is considered to be safe. Primarily though … memory foam has the most “problems” of this type.
The edge here goes to natural fibers and innersprings followed by latex followed by polyfoam with memory foam trailing on the bottom.
The comfort layers of a mattress are the durability “weak link” in most cases. Of the foams used here … latex is by far the most durable followed by high quality memory foam followed by polyfoam. In each type of foam … the higher the quality the more durable it will be (there are more or less durable foams in each category). Natural fibers are generally very durable although they do tend to take on a body impression to varying degrees. This body impression is not because the fibers are breaking down but because they are settling into the shape of the body and part of the design of the mattress. Microcoils and buckling column gels are also durable but less common.
In the support layers (and in general) … Latex is the most durable followed by innersprings followed by high quality polyfoam. All of these materials will usually outlast the comfort layers … at least if they are good quality (cheap innersprings for example may break or take on a set before a better quality comfort layer).
This in general depends on the construction and layering and/or zoning of the mattress much more than the materials used. Any good quality material in the right layering can produce good spinal alignment … although better materials such as latex or high quality marshall coils can do so over a wider range of sleeping positions. There is also a difference in how long the materials can produce this alignment with more durable materials doing so for a longer period of time.
While comfort and alignment can be produced with any material which is layered and constructed correctly for the individual … heavier weights certainly tend to wear out certain materials faster than others especially in the comfort layers. Polyfoam in the comfort layers should always be avoided except in the lowest cost budget mattresses, pocket or marshall coils tend to be the least durable of the innersprings (all other factors being equal), and lower quality memory foams are also an issue with durability. Side by side zoning using any appropriate materials are a good way to build a mattress when there is no probability of a “compromise” between partners with very different weights and sleeping positions.
By most standards … if a foam is certified by a reputable agency that lists what it is testing for … then there is little possibility of a foam being “dangerous” for most people … but the comments in the offgassing section would apply here as well.
In terms of the quality of foam … memory foam quality is determined by its density with about 5 lbs per cu ft being the rough “high quality” cut off. Memory foam under 4 lbs should be the last choice because they will be the least durable.
Used in the support layers … the minimum density of polyfoam used should be 1.8 lbs per cu ft with higher density being better. In the comfort layers … with the exception of the very lowest budget mattresses bought from an outlet that really knows the difference between different types of polyfoam … polyfoam should be completely avoided or at the most be an inch or less if necessary. Latex, unless it is mostly synthetic dunlop latex … is almost always high quality.
By excluding latex foam in this criteria (which in general is the highest quality type of foam which “passes” the most of your criteria) … you are also excluding the use of any foam at all that even comes close to the rest of your criteria and limiting your choices to an innerspring with natural fibers or to a mattress that is only natural fibers like an all wool or wool and cotton mattress or coir (coconut fiber) futon type of mattress. Unfortunately this also may not meet many of your criteria and is often less pressure relieving than good quality foam. Some of the innerspring under natural fiber mattresses are also ultra expensive as they are much more labor intensive in their construction and use higher cost materials and construction methods than cheaper mattresses of this type.
So my question would be are you truly excluding latex foam and looking only for a natural fiber with or without an innerspring type of mattress or were you “lumping in” latex foam with other foams because you thought all foams were similar?
Hopefully this “line by line” comparison of different materials will help you in your choices and understanding some of the tradeoffs involved in choosing a mattress and materials.
If you have more questions that I haven’t covered or need any clarification on any of this … feel free to post them
Phoenix
I live on Long Island, NY.