At least for now (I have been reminded several times that there is never only one way to do things).
I found that stitching paper with felt underneath was pleasant in terms of having more substance to slip my needle through (and bury the thread in), but the paper was ripping a lot more than when I just stitch paper! Add the fact that a piece of paper with a felt backing gives me fewer options for what I can do with it later, because it is thick and harder to glue onto something else, and my decision is easy.
A stitched piece of paper can be added to almost anything, including a piece of felt.
So I am abandoning my stitching on the felt backed pieces, which were my originals. I did scan them so I printed out some more pages, and am now sewing on them. It is fun to look for the differences, in the picture below, between the original painting with stitches applied to it, and the stitches I have just applied. They are very distinct to me. On the screen they are all just digital.
The beauty is that the edges which gave me some challenges before are now just printouts of the edges. SO, one can rip apart a painting and stitch it back together over and over, with as many layers as one likes; with holes, rips, folds, whatever ~ then scan it, and retain the look without the hassles.
Digital versions of stitched appliqué can be quite awesome.
On the other hand, I must admit that all those “hassles” add lovely texture!