Hi Gmeluk,
While Tempurpedic is certainly high quality memory foam and would be unlikely to be offgassing to any “unusual” extent … memory foam in general does have some rather nasty chemicals in it and some people are quite sensitive to it. The symptoms you are describing are typical of this sensitivity to memory foam. I myself have experienced similar symptoms with some memory foams but not others. My personal belief is that all memory foams “offgas” to some degree and while many are tested to be within certain “safe” tolerances … this does not mean that there won’t be some people that are sensitive enough to be affected. Besides offgassing … all foam will break down over time and the fine dust that would be produced by the breakdown of memory foam could also be an issue with some although this is not generally talked about as an “issue” and I am simply putting my own thoughts out there as there is no testing for this to my knowledge.
The Cloud Luxe (and the cloud series in general) are Tempurpedics softest mattresses and there are many cases where those who are over 200 lbs or so do not do so well with them. This would depend to some extent on overall sleeping profile and position but with 4.75" of soft memory foam … it is very possible that you are sleeping out of alignment which can certainly lead to back pain issues. Memory foam in general is the least supportive of all foams and for those that really like it compared to all other options … it is usually wise to use the thinnest possible layer that provides adequate pressure relief. While there are many good quality memory foams including the manufacturers listed on the Certi-Pur website … my personal favorite is the Aerus memory foam by Foamex. This is mainly because it is more breathable than most memory foams even though even “breathable” memory foam is not as breathable as other foams.
IMO … the material that has the best combination of pressure relief and support is latex foam. When used in the comfort layers, it’s pressure relieving properties (in the right softness for each individual) are at least equivalent to memory foam and at the same time it is the most supportive and durable foam available . Both Talalay and Dunlop latex are appropriate for a comfort layer and (in a firmer version) for a support layer in a mattress.
Most people prefer the Talalay latex in the comfort layers over Dunlop because it is available in softer versions which are “roughly” the same softness as most memory foams (although they certainly feel different). They also do not respond to heat like memory foam and you will not sink as far “into” the mattress. Latex is also more breathable and cooler than memory foam. Because of its elasticity, it also is very good at isolating motion between two sleepers. There is more information about the different materials used in the comfort layers and support layers of a mattress in the “mattresses” section of this website.
You can see my thoughts about them in post #2 here. They certainly fit the profile of the type of manufacturer that offers better quality and value.
I’m not sure exactly where you are but there are not too many manufacturers in that area. A few options that may be worth looking at if they are close enough are …
Store Locations - Room & Board Direct outlet for Restwell mattresses which offer a range of latex and latex combinations
http://www.healthyback.com/storelocs/storelocs.php Carries the Pure Latex Bliss (under the Healthy Back Bliss name) which are high quality talalay latex mattresses. They are good for testing different latex feels and constructions however they are priced too high for me to consider them a good buy.
http://www.savvyrest.com/news/2011/06/02/savvy-rest-natural-bedroom-opening-vienna These three carry Savvy Rest mattresses which are a “choose your own layering” latex mattress that is available in both Dunlop and Talalay. IMO … they are also priced too high to consider purchasing because several of the members here offer a similar mattress for much less but they are a good “testing ground” for different latex layering combinations.
Find an Original Mattress Factory Store This is a regional mattress manufacturer which makes a wide range of all types of mattresses including memory foam and latex which are high quality and good value. This would likely be your best choice for a “local” mattress purchase.
EDIT: There is a more complete list for the DC / Northern Virginia area in post #2 here and for the Baltimore area (with many duplicates) in post #2 here.
Other than this … the best option would be to use these outlets to narrow down the type of layering that works best for you and then duplicate it through an online manufacturer which offers DIY constructions such as several on this site.
A good place to start for a side sleeper in terms of the thickness of a comfort layer would be about 3" of high quality memory foam or softer latex (19 - 24 ILD is typical). Because you are slightly heavier than average … you may need slightly thicker and the firmer end of this range may work well. The support layer should be quite firm (36 ILD and above) to prevent some of the back issues you have described. In a 3 layer mattress … the middle layer may be slightly less firm (say about 28 - 32 ILD to help with a thinner comfort layer) with an extra firm bottom layer underneath it (40 - 44).
Of course these are rough guidelines as your personal testing will be more accurate than these guidelines but they will give you a place to start.
Given what you have said … I would strongly consider latex as an alternative to memory foam … and even though it is the most expensive foam material … when purchased from a high value outlet … even a very high quality custom layered latex mattress will cost you substantially less that the Tempur Cloud Luxe … and it will last you much longer.
If you have any other questions … either before or after testing mattresses … don’t hesitate to ask 
Phoenix
PS: Custom Comfort by Winn is a regional wholesale manufacturer who appears to make good quality mattresses however they only supply to stores and are not factory direct and they don’t list any latex mattresses on their site. They do have a list of retail outlets that carry their mattresses should you wish to test them out.