Yes, that tends to be an issue with paper pulp.  The paper swells when wet, then shrinks when it dries.  I believe David mixes in some calcium carbonate (ground chalk) with his pulp, which probably gives it a bit more stability.

Before you applied the putty, I would have covered the piece with strips of torn paper with a light application of adhesive, and burnished it down with the back of my fingernail or the back of a spoon.

When dry, sand any rough spots, and coat it with several coats of something like acrylic gesso to smooth it out.  Other things may work, too, but apply them with a brush, and make each coat quite thin; thick, heavy coats create their own problems.  Brush on your coating, let dry, sand; apply another thin coating, sand, and repeat as needed.

Sue

No, a thick layer of paper towel is likely to be too soft and just shred.  Fine layers are the answer.  There is a special method, developed by Nives Cicin-Sain (she has a gallery on this website) that gets incredibly smooth results.  She sells an e-book about her method but you need experience before taking it on.
Anyway, as I said, thin layers, firmly applied, burnished with the back of a spoon before finally dry, sanded, as little moisture as possible . . . . you should be able to get it smoother.  Good luck.

thank you very much for your kind encouragements

regards