In rescue training we were taught to support an injured climber horizontally while he was still hanging on the rope. From this postion, a stokes litter could be lowered or raised to the injured party, and moved into place right underneath him.
We would set up several prussiks and slings, and lay the climber out flat, supporting the ankles, knees, back, and head. The waist was already supported by the harness.
If you or someone were going to be hanging for some time, this would allow several support points, and probably great blood circulation, eliminating the "suspension trauma" problem.