Welcome to the Quilting Board!
Like JanRN and QuiltE I also PP'd the Farmers Wife and Pony Club quilts, 201 blocks in total (I think) I always remove the paper when I finish a block and if I need to align seams that maybe on an angle I will draw my 1/4 inch seam line on the fabric. I also remove the paper if I have to sew sections together as I loathe removing the paper from within a seam line. If you press well and use a little starch on your blocks you should not have any distortion but if you are worried you can sew a small line of stitched around the block. Hope this helps and I love your pattern..
I wait until everything's sewn together.
I don't remove the paper until the quilt is ready to sandwich.
I press & trim the block with the paper on it (no steam as it may shrink the paper) Then once the block is stitched into the quilt top I remove the paper. (I use a 1.5 length stitch & regular paper, just fold along perforations & the paper is easy to remove) The stay stitching on the quilt top edge keeps the blocks along the edge that are paper pieced from getting stretched.
The only time I would leave the paper on a block is if I have to join it to another block and match the seams of each. If you're going to sash the block, or if the block doesn't have matching seams ... I would remove the paper when the block is done and store the block flat.
May your stitches always be straight, your seams always lie flat, and your grain never be biased against you.
It was interesting to read all the suggestions - I have a paper pieced project to do at some point so enjoy all the tips and tricks. Sounds like no set rules but personal preference.