Hi Kristen,
Unfortunately there is no such thing as “the best” mattress in general terms (organic, vegan, non latex, chemical free, or otherwise) … there is only a mattress that is “best for you” based on all the criteria that are most important to you regardless of whether the same mattress would be “best” for anyone else (even if they have similar criteria).
There is more information about the 3 most important parts of “value” of a mattress purchase in post #13 here which can help you make more meaningful quality/value comparisons between mattresses in terms of suitability (how well you will sleep), durability (how long you will sleep well), and the overall value of a mattress compared to your other finalists based on suitability, durability, and all the other 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).
There is also more information in post #2 here and the more detailed posts and information it links to about safe, natural, organic, “chemical free”, and “green” mattresses and mattress materials and components that can help you sort through some of the marketing information and terminology that you will encounter in the industry and can help you differentiate between them and answer “how safe is safe enough for me” or “how organic is organic enough for me” so you can decide on the types of materials you are most comfortable having in your mattress. These types of issues are complex and are generally specific to each person and their individual sensitivities, circumstances, criteria, beliefs, and lifestyle choices.
There is also more information about the different levels of organic certifications in post #2 here and some of the benefits of an organic certification in post #3 here and there is more about the different types of organic and safety certifications in post #2 here and more about some of the differences between organic and safety certifications in post #2 here that can help you decide whether an organic certification is important to you or whether a “safety” certification is enough.
If you are only looking at organic materials (regardless of whether non organic materials may be just as “safe”) and have ruled out wool or other “safe” fire barriers and you have also ruled out latex then your criteria would be very restrictive and you would basically be limited to organic cotton (such as an organic cotton futon) which may not be the most comfortable choice or perhaps an innerspring mattress that uses organic cotton or other organic fibers as a comfort layer (and these will be somewhat difficult to find).
There is a list of of some futon options in post #2 here and there is also a list of some of the better innerspring/natural fiber options I’m aware of in post #4 here. You would need to check if any of them have a retailer that is near you (or that they sell online if you are comfortable with buying a mattress or futon that you can’t test in person before a purchase) and if an organic certification is important to you then you would also need to check with them to make sure that their natural fibers are also vegan and whether they have an organic certification and/or that they can make a prescription mattress that doesn’t pass the fire regulations. There is more about “safe” fire barriers in this article and post #2 here and the posts it links to at the end.
If you let me know your city or zip code I’d also be happy to let you know about any of the better options or possibilities I’m aware of that may be close to you.
Phoenix