Hi akb615,
Post #2 here includes a number of links to some of the better forum posts and topics about mattresses and children which include some guidelines for children and more information about many of the better options as well (including both of the mattresses you mentioned).
The thickness of a mattress in an upper bunk can be a safety issue and with children I would lean towards safer choices whether it was about the height of the mattress or about the relative “safety” of the materials in the mattress.
There are too many unknowns, variables, and personal preferences involved for me to make specific suggestions but there are some “possibilities” that are included in the children’s topics that would make good choices that are also 6" or less.
There is more information about organic, natural, “chemical free”, green, and “safe” materials in post #2 here and the other posts it links to that can help you decide which materials you are comfortable with having in your mattress and that can help answer your questions about “how safe is safe enough for me?” because these types of issues are complex and are generally specific to each person and their individual sensitivities, circumstances, and specific criteria.
I would want to know the specifics of their bunk mattresses (see this article) because the polyfoam in the comfort layers of the RoomandBoard mattresses is generally lower quality/density than I would be comfortable considering.
I agree with MFC Memory Foam Comfort that a futon type mattress (including cotton futons) can also be a good choice for a child and for your circumstances because they they are generally thinner and firmer (children generally need firmer mattresses) as long as you are comfortable with the fire retardant methods that they use. There are some options for futons that are included in post #2 here that may be well worth considering and it may also be worth considering the Tuft & Needle Five (see posts #2 and #6 here for more about the materials they use).
Phoenix