I think the backwards one would get in the way of maneuvering the quilt. I've seen recommendations for the saddle chair (without arm or back) for use with a frame - and I think it does allow the sitter great flexibility to move around/along the frame.
Does anyone remember the 'chairs' where you rested your shins on the lower padding - and had no backrest. We had one for years with our computer desk, though now I'd probably fall on my face trying to stand up from it.
Cheers, K