Hi morning kinks,
There are some hi-low adjustable beds (which are also position adjustable) here which go as low as 7" and have up to 19" of travel. I’m suggesting this just in case they may offer an alternative that would work with the lift better.
Kopavi has already suggested a couple of very good options (thank you :)) for 6" or less of latex and there are also a few more in post #4 here.
If I was limited to 4-6" then it doesn’t leave much room for separate layering and if 6" is possible then that would certainly be better. I would tend to use all latex either Talalay or Dunlop both for performance reasons (it will have a greater range of softness to firmness in a thinner core) and for durability reasons. Which firmness level or combination was best would of course depend on your uncle’s weight and the outlets that I linked to would provide good advice to help you make the best possible choices.
With a 6" mattress … then a single 5.5 - 6" core of Dunlop would work well because Dunlop has a higher sag factor (it gets firmer faster with deeper compression) so a softer core would still provide good support as it was compressed. Alternatively a progressive layering of Talalay (3" of softer over 3" of firmer) can also provide for a softer layer on top and a firmer layer below so this would be equivalent to a higher sag factor as well if he liked the feel of talalay better.
You have some good options and I would talk with the manufacturers that offer what you are looking for to get a sense of the layers (and of course the cover) that may work best for you.
Phoenix