The Temurpedic site lists some of the “quality” specs of their mattress and in many cases these involve multiple layers of different density memory foams. for example the Rhapsody uses both 7 lb memory foam and 5.3 lb memory foam. The cloud series uses 4 lb memory foam in combination with 5.3 and 7 lb memory foam and there are even different versions of the same foam density (softer and firmer formulations of the 5.3 lb foam for example).
In addition to this … they don’t list the “comfort” specs of their materials and there are hundreds or even thousands of different types of memory foam with different performance characteristics and feels … even in the same density. Some of the variables in memory foam are listed in post #9 here. Every layer and component in a mattress affects every other layer and each individual person can interact with a mattress differently from someone else so unless two different mattresses have the same materials and components … it can be surprising how different some seemingly minor differences can make. While foam density can be a “quality and value” comparison … it has little to do with how a mattress feels and performs for any individual person. This is made more difficult by the fact that many of the descriptions on the WalMart site are incomplete.
What this means is that there is no way to “match” one memory foam mattress to another unless a manufacturer has done extensive testing or has a lot of experience in comparing the Tempurpedic line to the mattresses they make. For example … Select Foam makes a line of mattresses that are designed and tested (real world testing) to come very close to the Tempurpedic line but in most cases outlets that compare themselves to Tempurpedic are comparing apples to oranges.
The Rhapsody (which you like) has 1.2" of 7 lb memory foam over 2.8" of 5.3 lb memory foam over a base layer which is in the range of 2.2 lbs but has an unknown ILD (which is a comfort spec and has nothing to do with quality). This means that you would probably increase your odds of finding something similar if you found a mattress which had similar memory foam densities and layer thickness but even then the different memory foams may have completely different response rates, breathability, temperature sensitivity, and softness/firmness levels.
Your second choice the Contour Signature uses two different layers of 5.3 lb memory foam (1.6" and 2.4") over the same polyfoam so the memory foam thickness is similar but the memory foams used are different. both of these are listed as “medium-firm” but this is really a subjective rating and only really applies relative to other Tempurpedic mattresses because each manufacturer can use these “words” differently and there is no specific definition of these words.
The Cloud line uses various combinations of 4 lb memory foam with 5.3 lb or 7 lb memory foam (thicker layers as you move up the line).
With the guidance of someone who had compared a specific mattress to a similar Tempurpedic mattress then you would have better odds of “matching” the two but this level of expertise doesn’t exist at Walmart. instead … they have a money back guarantee which means you can “roll the dice” and get a refund if you’re wrong.
So looking at the WalMart website … almost all of the mattresses use lower density memory foam (usuallyin the 3-4 lb range) and the ones that are higher quality use different layer thicknesses (usually 3"). The one’s I would probably be most tempted to consider if I was in your shoes though because they are higher quality (but unknown in terms of how they may feel to you) include …
http://www.walmart.com/ip/Nature-s-Sleep-The-Aruba-12-Visco-Memory-Foam-Mattress-Set/15807203 This uses 3" of 5.6 lb memory foam and also uses 2.2 lb base form. It is supposed to be “next generation” which usually means it is more breathable and cooler than other memory foam. Foam is CertiPur certified.
http://www.walmart.com/ip/Nature-s-Sleep-The-Bermuda-11-Visco-Memory-Foam-Mattress-Set/15807146 Similar to the Aruba except it uses 4.6 lb memory foam and has an inch less in the base foam.
http://www.walmart.com/ip/Boyd-Eco-Lux-Gel-12-Memory-Foam-Mattress/21388843 They don’t ist the density of their memory foam but it uses 3" of it and another inch of convoluted memory foam under this. Also CertiPur certified. You can see more information about it here.
http://www.walmart.com/ip/Renew-10-Inch-Luxury-Memory-Foam-Mattress/17431684 This has 5" of 5.25 lb memory foam over a 5" HD base foam (don’t say the density). They are also good quality and CertiPur Certified
http://www.walmart.com/ip/SPALDIN-Memory-Plus-Foam-Mattress/21066279 these are somewhat unusual because Spaldin is an interesting manufacturer with some good information on their site that does several things differently from other memory foam manufacturers. The first of these is that they use MDI instead of TDI to make their foam (which is considered by many to be a higher performance memory foam that is also safer and less toxic method of making memory foam). The second is that they replace a much higher percentage of their petrochemical polyols with plant based polyols (about 50%) than most manufacturers and finally they aree Oeko-Tex certified rather than just CertiPur certified which is a more stringent standard oftesting for VOC’s and harmful ingredients in their mattress. They are the only one in North America that I know of whose memory foam is Oeko-Tex certified. the “down side” is that their memory foam is only 3.75 lbs.
So this will give you an idea of what I believe are the higher quality memory foam mattresses on the WalMart site. While it’s impossible to know how they will feel except perhaps from reading various online reviews which say how different people felt on the mattresses (and taking these with a grain of salt because each person has their own unique perceptions) … at least these have better odds of throwing the dice and coming up with a winning number