This has been a major work in progress. It is still not done, but it is a working prototype. It does what I need for now. I used cut disks of MDF and glued them together to make the drum. I then turned it as true as I could.
To lift the bed (creating the thickness) I have a large threaded rod and a bolt. I don't like having only one point to raise and lower the bed, as it is not very stable, but I will find a way to fix that in the future.
If you have any thoughts/suggestions, please feel free to share them with me.