Why not try your interfacing technique and see if you are happy with it? I would think it should work, though you might have a challenge of getting your pattern traced accurately.
Switching to fabric could lose some of the stability that the paper provides, when PPing.
What about using paper, then put a piece of starched fabric on top, held in place with a few lines of long stitches. Then PP in the traditional way overtop of the paper/fabric square.