Ok, everyone. Are you ready for this? There's a roll of very thin semi-transparent white stuff for sale at Lowe's, called "Sediment Shield for Trenches", which was recommended to me by a quilter I know for use as a foundation for a selvedge quilt I am making. It is very inexpensive (the roll I got is 24" wide by 300ft long--it comes in different widths, etc.) and weighs next to nothing, and doesn't have to be removed. This quilter had made a selvedge quilt using muslin as the foundation, and was unhappy with how heavy the finished quilt was. I have been cutting 12" squares and using them for a foundation for my selvedge quilt, and it works fine.
One of these days I plan on trying it for paper piecing. It's very thin and I'm sure I'll have to hand trace each block pattern onto it, but I still think that's preferable to having to remove all that paper. Not sure how it'll work for that, as it's not stiff at all...