I spray the parchment paper with some cooking spray, then put the "folded, not kneaded" dough/glop right on the paper to rise. Just leave the paper long enough to lay on top of the dough and put a towel over it to keep it warm and cozy. When the vessels are hot and the dough has doubled in size, just lift the whole thing by the paper edges and place it gently in the vessel and put the cover on. the paper may get a little brown, but you don't have to worry about it burning (if that concerns you).
Found a couple of proofing baskets today (wicker) at the Goodwill store for $.80 and $1.90 each to use with my La Cloche Oblong Baker when it arrives. I'll post pics of the whole sequence when it gets here so you can see how the parchment paper works.
Joe