R.M.
When my daughter (who is now 2) was an infant, I used one of those sleep positioners that was essentially two foam triangles connnected with a piece of fabric. She, like yours, was uncomfortable on her back but I found that she slept much better when I put her on her side, using the positioner to make sure she stayed that way. You could also use it as a transition method to get her accustomed to back-sleeping.