Grandpa17,
In my earlier reply, I was suggesting to make a 4-1/4" "filler" piece made of dense Styrofoam, covered in some kind of upholstery fabric, vinyl, or even interior-matching leather if you want to get real fancy. The right kind of Styrofoam will not give, crush, or crumble from the weigh of a human. It would also be extremely light weight.
An alternative to Styrofoam is foundation insulation. It is sold in 2" thicknesses and in 2x8 and 4x8 sheets. Some types might crumble a little over time, others surely not at all. Go to your all your home improvement centers to examine the various material choices. The material is extremely light weight and also very affordable. You would have to glue 2 pieces together to get 4", then add 1/4" light weight luan to complete the thickness. Maybe glue the 1/4" luan in-between the two for a good sandwich. Cover the sandwich in a zippered fabric or vinyl cover would make it very nice, and being zippered, you can easily replace the core material if needed. Phoenix may be willing to make a matching interior zippered cover to your specification, especially considering your dissatisfaction with your bed. You are doing their engineering for them.
Foundation insulation is designed to withstand the weight of earth against concrete basement walls. If it won't crush under that pressure, I think you won't crush it either.

Handling a fabric-covered light weight block won't be intrusive like a wooden box. You can toss it round effortlessly and it won't bang up your interior either.
BTW: Nice Diagrams!