Any ideas on creating a firm surface on top of a bed for exercising?

I normally use a pad on a rug on a hard floor but due to knee issues am not going to be able to get down (perhaps down will be OK, but getting back up will be a problem).

I am trying to jerry rig a surface similar to a PT table with the firm base and decent padding on top but on top of a mattress. ¾” ply as a bed board covered with some sort of yoga mat? Any creative thoughts? I don’t want to permanently damage my lovely guest bed.