So a family member is having back issues due to sleeping on a medium-firm pocket spring mattress. They actually find it better for their back to sleep on the floor.
Is there a queen mattress, preferably foam only, that is super firm - almost as firm as couple of blankets on a thick carpeted floor?
If it's a one sided mattress you can try turning it over and sleeping on the side with no comfort layer. Maybe add a topper of it's too firm.