I thought I’d add a few comments regarding your post that I hope will be of assistance.
By far the best advice you can receive is from your own experience trying out any product you are considering, as well as learning about mattress componentry and assembly. In this respect, the mattress buying tutorial on this site is quite helpful. Expecting someone to recommend a brand (out of hundreds) and a specific model (out of tens of thousands) from a brief description posted here would be unrealistic, and personally I wouldn’t trust someone who stated they had the perfect mattress for you based upon this brief data. Quite often they could be recommending what is best for them to sell, not what is best for you to sleep upon. 
You kept your Sealy longer than it was designed to last. The 6-8 year comfort life is common these days, and I see many products holding shape for only 4-5 years. This is why it is important to understand componentry and ask for higher quality foams. A good quality mattress with better componentry should give you an expectation of a ten year comfort life - I think that’s fair. While many people keep their mattresses longer than this, a decade is a realistic timeframe if the product is using higher quality componentry.
The term hybrid has been so twisted these days as to not have a true meaning. Originally coined by Mark Quinn at Leggett and Platt, it was meant to represent a true memory foam mattress where the polyurethane foam core was replace by a marshall innerspring unit. These days, you’ll have manufacturers calling any product with .5" of memory foam a hybrid. Focus on the componentry and feel and not the label (hybrid, Eurotop, pillowtop, etc.). If you do not like the feel of visco-elsatic foam, then you would probably be best off avoiding true memory foam mattresses or innerspring product that utilize a high percentage of memory foam in their construction. Again, your opinion when trying them out would be the ultimate decider.
Your concerns about offgassing would be more appropriately addressed to the foams within the mattress as opposed to the fire resistant barriers most brands employ. I posted a bit about these FR barriers here, and that information may be helpful to you. Most brands these days use FR barriers that are rated as non-toxic, although some brands will advertise theirs as more “natural” than others, and it can be a bit misleading. You’ll find many brands using wool as the FR barrier when getting into some of the higher-end latex beds, but I don’t think these will tend to be in the price range you mentioned. A mattress will still offgas if it has a cover or not. You can look for terms like CertiPur-US, Oeko-Tex and GreenGuard (numerous links on this site explaining what these terms mean) as types of certifications that test a mattress for VOCs. Regarding most of the mattress protectors using polyurethane films, you’ll find the majority of these films being produced in China (some protectors assembled in the USA). There certainly are exceptions, but that’s where most of these films now originate. And regarding “organic,” many brands are deceptive in quilting in the words “organic” or “Bamboo” or the like into their ticking, knowing that consumers will tend to think that these products are more natural/better. Look for a GOTS certification on the cover for it to be organic certified.
These are 14 year old torsion modular foundations (if it is a Sealy Posturepedic product). They need to be replaced. Torsion systems fatigue over time and are inappropriate for most current one-sided mattress offerings and will void most warranties immediately.
Again, focus on quality materials and I strongly recommend trying out a product before making a decision. Consumers spend an inordinate amount of time focusing upon the warranty and “what ifs,” and the mattress industry knows this, often using the warranty as a marketing tool. If you have a product using high quality componentry and it’s assembled well, warranty won’t be an issue. I wouldn’t make the potential of a company going out of business as a primary concern when choosing a product. Simmons went bankrupt a few years ago, so did Spring Air - at the time two of the top four mattress companies. They’re both still around, but no one can predict the future. If you do have a true warranty issue, they usually happen early in the life of the product, and in that situation I’d be more concerned with the reputation of a retailer and their track record of assisting consumers and making things right.
That’s an excellent first step!
Good luck!