Hi Var,
Welcome to the Mattress Forum! 
The mattress shopping tutorial (which is where I would start your research) includes this link to a thread that lists some of the better online memory foam providers that I’m aware of. Most of them are very familiar with the various Tempurpedic mattresses and would be able to tell you which of their mattresses are closest to a particular model in the Tempurpedic lineup and some of them sell a mattress that is specifically designed and listed on their sites as being closely comparable to the Rhapsody Luxe or the Rhapsody Breeze. Post #9 here and the posts it links to also has more about the different ways that one mattress can “match” another one which you can use as a reference in your conversations with them, and post #2 here also speak to three steps to help you match on mattress to another.
Some of the old Tempurpedic specifications are listed here. While older, there’s a bit more information about Tempurpedic mattresses and their layering in this post that you may find interesting.
The “old” Rhapsody used:
1.2" tempur HD in the top layer: 7.2lb/ft3
2.8" of Tempur support foam: 5.3lb/ft3
(2) 4" 1.8lb/ft3 density base layers with air crate tops
The “modern” Contour Elite Breeze does use 7 lb and 5.4 lb memory foam in a similar configuration to the old Rhapsody.
Off the top of my head … Novosbed (in their medium firmness level), Rocky Mountain Mattress, Tempflow, Foamorder, and Christeli all make at least one or more mattresses that use 5 lb or higher memory foam but you would need to check their websites or talk to them to find out how they compared to any of the Tempurpedic mattresses.
The component post here has some sources for memory foam components. In addition to the online members of the site listed in the previous membership link … post #12 here has some of the better online memory foam options for those who are looking for a memory foam mattress. I don’t keep a listing of all of the current offerings of the densities of memory foam being offered by manufacturers listed here on the site, as it would simply be too large of a task for any one person to accurately accomplish in a market that is constantly changing.
Hopefully that gives you a good start.
Phoenix