There are some mattresses with no memory foam in them and I will steer you there. This particular mattress also has an interlocked coil system, which is something he will need. As his condition progresses, it will continually become more difficult to get in and out of bed, so the mattress needs to be stable...more so than a mattress with an individually pocketed coil system.
The individually pocketed coils tend to be more comfortable, but we'll take care of that also.
These are Sealy mattresses, not Posturepedics. They use the older Posturepedic coil system and are reasonably priced.
Add to both of these, a latex topper. You will note that these mattresses differ in height by 1/2 inch.
So, you would get a 2" topper for his mattress and a 1.5" topper for yours and both beds will be even in height.
The toppers grip the mattress and don't shift or bunch up.
Here is the link for the toppers.
Finally, for your cherry bedstead. Replace the framing, (side rails and slats), with a steel replacement rail set that has all the center support you'll need, which includes legs to the floor to keep it from bowing. You'll sacrifce the cherry side rails, but be able to keep the headboard and footboard.