Hi lawsonmh15,
Just to keep things a little simple … I’ll go through a few of the “specs” of memory foam and how they work. I could give you some very technical links but they will probably do more to confuse than help 
First of all … I would completely “delink” density with everything else except durability. Polyfoam (and memory foam) density has little to do with softness or firmness. It’s primarily a matter of how much material is in the foam and the composition of that material vs air content. The primary benefit of density is durability. Higher density memory foams in the 5 lb range and higher will be the most durable, medium density memory foams in the 4 lb range will be less durable but may be preferable for some people because of the differences in how some of them feel and perform, and I would avoid any memory foam that is less than 4 lb density unless you are in the lowest budget ranges because of potential durability issues. Ultra high density memory foams in the 6 lb range and higher may be slightly more durable yet but the benefits of greater durability begins to level off above this range.
Any density of foam can be made in either softer or firmer versions so you could have low density firm or soft and high density firm or soft foam.
The polymer density of memory foam or it’s “pure” density before any fillers or other materials are added is also important. Fillers can be added to memory foam to alter it’s performance and properties, increase fire retardancy, lower the cost, ease of manufacturing, or for many other reasons and can increase the density and give it a “false density” but can also lower the durability of the memory foam. These fillers can include silica, carbon black, calcium carbonate, various clays and even gel particles, all of which can give the memory foam a higher total density than the polymer density of the foam before the fillers are added.
In the case of memory foam there are also other factors that are independent of density.
Breathability: this is determined by how open celled the foam is. The more the cells are open … the easier the air moves through the material which can make the foam faster reacting. While it’s true that in general … lower density tends to have more open cells … this is only a loose relationship and high or low density foams can be either more or less open celled. More open celled foams that allow for more air circulation tend to sleep cooler.
Viscosity/elasticity ratio: Viscoelastic or memory foam is partly viscous (meaning it flows away from pressure like a liquid) and partly elastic (meaning it compresses under pressure, stores energy and bounces back). Any density of memory foam can have either more or less viscosity or more or less elasticity. In general though … the chemicals that give the foam more viscous qualities (memory foam like) are heavier so lower density memory foams tend to have less “memory” and tend to be faster reacting.
Temperature sensitivity: Viscoelastic foam goes through a transition from elastic to viscous within a certain temperature range. Foams that are more temperature sensitive will be firmer when they are cooler and softer when they are heated by the body or the environment. Humidity also plays a role here (higher humidity softens it). Memory foams that are less temperature sensitive will tend to have less of a range of softness and firmness. foams that are more temperature sensitive will be both firmer and softer depending on the degree of softening and transition into viscosity from elasticity.
Softness: This is determined by the formula of the foam, its temperature sensitivity, and of course is also dependent on body and external temperature, humidity, and time spent on the foam. Some foams have a range of very firm to very soft while some start off softer and never get quite as firm. All memory foams, even the ones that are firmer than others (they range from an ILD of about 8 to about 18 although ILD is not that significant with memory foam), are considered to be soft foams and the biggest variable is how long it takes for them to get soft. This is why memory foam cannot be used as a support material in a mattress (it’s only used in the top layers) and there is always a different material used under the memory foam to support the weight of the body. Memory foam is a slow responding pressure relieving material only. Because memory foam is time dependent and also depending on the speed of compression … It takes more pressure to press down on memory foam that it exerts coming back up and ILD is measured after a time delay which is another reason it can be so misleading with memory foam.
Response rate: Like any liquid … firmness and softness will depend on how quickly you compress it. If you press quickly on water or honey for example … it takes “time” for it to flow away and will feel firmer than if you press it much more slowly. Denser foams tend to be “slower” in response although the other factors mentioned previously can modify this as well.
Pressure relief: This is connected to both softness and density because higher density foams can “melt” into shapes that more closely fit the body which means they distribute weight better and lower the pressure around pressure points. They can take more time to “melt” though so with initial compression or with movement they can feel much firmer. This is why Tempurpedic says that their 7 lb foam is the most “conforming” even though their 4 lb foam is the “softest” (gives more with initial pressure).
These are just a few of the factors that can be included in a foam’s composition and which results in different memory foams that “feel” very different … even if the density (durability) is the same.
Tempurpedic for example has two versions of their 5.3 lb foam one of which is softer feeling than the other. In general … their 4 lb memory foam feels the softest … their 7 lb foam is the next softest feeling, and their 5.3 lb foam is the firmest. The 7 lb foam though … because it is denser … can feel firmer until it softens.
The denser memory foams are also more expensive in general to produce so tempur 7 lb foam is more expensive than their lower density foams and this will be reflected in the price of their mattresses (along with the thickness of the memory foam layers).
The thing to remember is that you want a memory foam with your preferred “feel” in the density that is appropriate for you. If you use a density that is to low … the foam may feel great for a while but it won’t last and it will lose it’s feel much faster.
Typically memory foams are described by density (which translates into durability), breathability (how open the cells are and other methods that are used to make it more breathable which results in cooler or warmer sleeping foam), temperature sensitivity (the range of temperatures it is most sensitive to and how soft or firm it becomes in certain temperature ranges), response time (how quickly it adapts to new shapes and how much of the “sleeping in wet sand” feeling it may have), and the overall feeling of softness or firmness (a general impression that most people would share based on a combination of many of these factors)…
So the link you provided earlier was a 4 lb memory foam which IMO would not be suitable for you in a layer that was 3.3" thick. It would lose its properties far too quickly. I would also not recommend any of the cloud series unless you were willing to trade the feeling for lower durability. In the same way I would not recommend the iComforts partly because the gel foam has a polymer density closer to 4 lbs and partly because the “softer” models use comfort layers that are rather thick and you would be risking good spinal alignment (although the showroom feel is nice). With memory foam … thinner layers are better than thicker layers and I be very careful with memory foam layers more than 4" thick.
At Rocky Mountain I personally would look at their regular memory foam mattress and the mattresses they list in the component beds section such as which may be a good option as it only has 2" of 4 lb density and another 2" of 5.3 lb density and the layers (both memory foam and support layers) can be re-arranged to change the feel and support levels. Another advantage to this type of layering is that a single foam layer can be replaced without having to replace the entire mattress.
If you want a mattress that is made to “resemble” the tempurpedics and that uses similar quality foams … then some of the options in the online memory foam list here may be worth considering.
Many manufacturers claim that their mattresses will “duplicate” a tempurpedic at very low prices but while similar quality memory foam mattresses can be purchased at significant savings … the cheapest memory foam mattresses are usually not worth considering and their “comparisons” to tempurpedic can be very misleading.
Everything is a matter of tradeoffs and there’s nothing “wrong” with buying a lower density memory foam for the sake of either price or “feel” as long as you realize that you would be giving up durability and don’t “buy into” misleading comparisons. There is more about the different ways one mattress can match another one in post #9 here.
Phoenix