Hi wheezer,
I would keep in mind that all materials have softer and firmer versions and designs so that you don’t relate firmness or softness to a material or to a platform but instead to a certain mattress design. The steel base of the Serta for example (which you can see here and here) is just as “firm” as most other platforms. The difference in what you feel is in the mattress design (unless the foundation has flex and the mattress is thinner in which case it will also have an effect on how the mattress feels and performs).
They certainly struck me as “good people” but I would personally never buy a mattress where I didn’t know the details of all the layers … and this would be especially true if I had MCS (assuming that is true in your case) because it would introduce another very important reason to know besides just the quality and value of the mattress. Having said that … only you can decide on your own personal risk tolerance. Serta also doesn’t disclose the details of what is in their fireblocker fire barrier to my knowledge (they just say that it’s safe without any details which doesn’t answer the question that is particularly important for MCS sufferers which is “how safe is safe enough?”). Graphite is generally an additive to foam or a surface treatment and may be one of the “ingredients” but there would likely be more as well. If you have MCS you could also get a doctor’s prescription to have a mattress made with no fire barrier at all although I don’t know if they offer this level of “customization”.
There is also a forum member that has created a site with some excellent information about MCS and ways of dealing with it which you can see in post #4 here. It may also help you know what to look for that may be important (such as the glues or surface treatments used in foundations or mattresses or fabrics).
I don’t know the design details of your bedframe, how strong it is, how it supports the foundation or box spring, or why it’s falling off but it seems to me that if adding slats is practical that it may be a very good idea if the rest of it is still strong. A mattress needs good support and I certainly wouldn’t want a bedframe where the foundation or boxspring was falling off.
Overall though with your sensitivities it would make it even more important to me to know what was in my mattress than less and while it’s of course important to deal with good people with good transparency and knowledge … my “trust” would be based on their ability to provide me with the specific information I needed or wanted to know.
Phoenix