Hi JLJ:
Welcome to the Mattress Forum! 
Very good – you’re taking the proper steps in making an informed mattress decision!
It is required is that a mattress pass the 16 CFR 1632 and 1633 fire regulations with or without the use of fire retardant chemicals (the method of passing the regulations isn’t specified in the regulations). The most common method used to pass the regulations is the use of inherent fire barrier fabrics that are either quilted into the cover or are wrapped around the inner materials of the mattress like a sock. There is more information about fire retardant methods that are commonly used in the industry in post #2 here and in post #4 here (which also has some information about potentially obtaining a mattress without any FR barrier with a prescription from a health care individual). I would consider the more common viscose/silica fire barrier to be a very safe material, and of course would have the same opinion about wool. If your personal preference is to use something other than an animal product, then you most likely FR barrier would be a viscose/silica blend.
They use the inherent rayon/silica barrier.
I don’t have the particular specifications of each mattress you listed, but the latex Berkeley Ergonomics uses is very high quality Vita Talalay from Radium Foam and it is Cradle To Cradle Gold certified – the only Talalay in the world to have this certification. They also use GOTS certified and Oeko-Tex certified organic cotton and GOTS certified and Oeko-Tex certified organic wool. These items would have passed strict testing for VOCs and harmful substances, so I personally wouldn’t have any concerns for off-gassing of these specific materials.
I’m guessing you’ve read this already but for the sake of others that may read your post you can see my comments about the Old Bed Guy and his website (and some of the very strange comments he makes) in this topic. There is “some” good information on his site and some information that is questionable at best and misleading, inaccurate, or deceptive at worst. While many people may be happy with one of his Charles P Rogers suggestions (and you can get a backstory in the previous link as to one of the reasons he recommends them so much) … there will always be some that won’t be as well (see this topic as an example).
While other people’s comments about the knowledge and service of a particular business can certainly be very helpful … I would always keep in mind that you are the only one that can feel what you feel on a mattress and I would be cautious about about using anyone else’s suggestions, experiences or reviews on a specific mattress (either positive or negative) or review sites in general as a reliable source of information or guidance about how you will feel on the same mattress or how suitable or how durable a mattress may be for you. In many if not most cases they can be more misleading than helpful because a mattress that would be a perfect choice for one person or even a larger group of people in terms of “comfort”, firmness, and PPP (Posture and alignment, Pressure relief, and your own Personal preferences) may be completely unsuitable for someone else to sleep on (even if they are in a similar weight range). In other words … reviews or other people’s experiences in general won’t tell you much if anything about the suitability, quality, durability, or “value” of a mattress for any particular person (see post #13 here).
There really is no one “best” type of mattress, but more importantly, finding the components that “best” do what you’re desiring them to do and are most appropriate for your specific application. You’d want to make sure that the materials in any mattress you’re considering would meet the durability guidelines here relative to your weight range … the choice between different types and combinations of materials and components or different types of mattresses are more of a preference and a budget choice than a “better/worse” choice (see this article). The best way to know which types of materials or mattresses you tend to prefer in general terms will be based on your own local testing or your own personal experience (which is possible for you with the Berkeley Ergonomics, but not with the Charles P. Rogers mattresses).
These are questions that only you can answer for yourself as to the appropriateness of any particular product. The platform bed you mentioned seems to be made of quality materials, although I can’t ascertain what is used for the deck pieces. Most of the major adjustable bed manufacturers put out a good quality product, so I wouldn’t necessarily have a concern about any of them being “trouble.” It really comes down to if you think that the advantage of being able to adjust the head and foot section of your mattress is desirable and if you’d use it enough to make the extra price worthwhile to you.
If you’re simply concerned with slight elevation, a wedge can work well, provided the wedge uses foam of a high enough density and ILD, and the angle is appropriate for you.
An all-latex mattress will generally conform better and last longer than a typical innerspring mattress when used in an adjustable bed configuration.
If you have a solid surface support system under their mattress (like when being placed upon solid decks) then something like a this coir bed rug could be placed underneath the mattress and it would increase ventilation under the mattress as well as reduce the chance of moisture being trapped under the mattress. A solid surface support system that doesn’t provide any ventilation underneath the mattress can add to the risks of moisture retention and developing mold or mildew or dust mites in a mattress but if there aren’t any additional risk factors involved then it should be fine. A bedroom in a basement would be more likely to have issues than one on the third floor. Increased air circulation can also assist with temperature regulation.
Just in case you haven’t already read it, the first place to start your research is the mattress shopping tutorial here which includes all the basic information, steps, and guidelines that can help you make the best possible choice … and perhaps more importantly know how and why to avoid the worst ones.
Two of the most important links in the tutorial that I would especially make sure you’ve read are post #2 here which has more about the different ways to choose a suitable mattress (either locally or online) that is the best “match” for you in terms of “comfort”, firmness, and PPP that can help you assess and minimize the risks of making a choice that doesn’t turn out as well as you hoped for and post #13 here which has more about the most important parts of the “value” of a mattress purchase which can help you make more meaningful quality/value comparisons between mattresses in terms of suitability (how well he will sleep), durability (how long he will sleep well), and the overall value of a mattress compared to your other finalists based on all the parts of your personal value equation that are most important to you (including the price of course and the options you have available after a purchase if your choice doesn’t turn out as well as you hoped for).
I hope that’s helpful!
Phoenix