Haven't done regular paper piecing but I'm just about to get to a curve (significant but gentle) on my English PP project. I'll have to snip my paper as I go but no reason it shouldn't work.
When sewing unfamiliar curves I usually mark a few match points when I cut them -- using chalk or tailor's tacks if the seam allowance is narrow. Then just a matter of notching or clipping the seam allowances as needed (usually AFTER sewing) to get it all to lie flat. Sometimes just pressing is enough. If you make the pattern again, I think you could successfully piece those curves.
