Hi, my thoughts were pretty slow in gathering, but have had this in the back of my mind since first reading your post. The idea of felting over a "found print" is intriguing. Like you though, would not be happy with the paper stuck in with the wool.
When I've used a "pattern" to develop a design in felt - like an applique or a picture- it worked to trace the main lines and then cut it out each part on a piece of tag board - the part felt is open and the tag board is like a page around the open area. Then felt in the open area. when the color is going nicely, move onto another piece and needle that color in place.
Keep the original "found pattern" intact and infront of you so you can see it to help develop details.
For the appliques already done - seems you will be stuck with the paper-- unless it disolves with the wet felting - some napkins almost melt when wet so maybe?
Soft needle felted appliques needle into soft wools or wool felt very nicely. You can also make larger needle felted or wet felted items such as mug coasters, seat cushions -- make thick circles and then needle the appliques into the needle felted item -- thus you do not have to make the design go all the way through a thick felt.
HTH - would enjoy hearing what you finally decided to do with your appliques.