Hi rockyrusso,
I can certainly understand how frustrating it can be to test hundreds of mattresses and still not really know if you are any closer to your ideal mattress or know which of the “stories” you can really trust. This is unfortunately the “norm” for most people when they are mattress shopping and it’s remarkable how many final choices are really made based on mattress shopping fatigue and the desire to just get it over with.
That’s fairly general because almost all mattresses have foam stuff of some kind or another … either polyfoam, memory foam, or latex foam.
Assuming that what you were testing really was latex and not just what someone was calling latex (which is amazingly common) … this points towards slow recovery materials like memory foam instead of fast recovery materials like latex or polyfoam in your comfort layers (the upper layers of your mattress).
Well that certainly solves a potential problem 
There are also some mattresses that have side to side spilts where each side can be custom made to different specs but this is more common with latex.
The Rhapsody uses high quality 5.3 and 7 lb memory foam (and of course a high quality base polyfoam layer). The 7 lb memory foam is actually softer than the 5.3 lb so this may be a good compromise between you. Tempurpedic is good quality but is not good value (there are other mattresses that use the same quality materials that are much less).
The Genius is one of the firmer of the iComfort line and if you liked it as much as the Savant which is on the softer end of the line I would suspect that the mattress you tried had been on the floor for a while and the polyfoam in the Genius has significantly softened (see post #2 here). Like the Tempurpedic line, the iComfort line is also low value (and you can see an analysis of the line in post #11 here) but for different reasons. It uses much lower quality foams and and many of the models have low density polyfoam (like the Genius) which would be subject to early softening and degrading. The quality is lower and the prices are still much too high for the quality of the materials they use.
Yes they are very different in both quality, price, and layering, but they both share the fact that like the other major brand mattresses … they are poor value.
The most important first step is to connect with the retailers or manufacturers that have the knowledge, experience, value, and service that can help you make your best choices. Finding better outlets can be more important than finding a better mattress when you are starting out. The best choices in most mass market outlets will likely be poor quality and or value while almost any choice at a better outlet where you can work with someone who knows what they are taking about and will put your interests above their commission or profit margin will likely be a more suitable and better quality/value choice.
Post #3 here has links to the better possibilities in New Orleans I’m aware of as well as along the Gulf Coast.
Post #12 here includes a few of the better online memory foam options incuding several of the members here. One of them makes a line of memory foam mattresses which is equivalent quality and feel to the tempurpedic line and one can work with you and customize a mattress to your specifications if one of their models isn’t quite right.
If the local outlets don’t have the quality, value, knowledge, or experience that you want or trust (and some of the things to look for in a better outlet are in this article) … the online options can be a great source of value and they are very good at working with their customers and using your local testing along with “averages” to help you make the best possible choices.
Phoenix