You just need to trace your design onto the fabric sheets now and start piecing. You might be able to iron them to freezer paper and run through your printer to get the pattern onto them. Some printers can handle odd stuff like that and others will just give up.
You would leave the fabric sheets on the blocks instead of pulling them off like paper-piecing.
I do paper piece quite often but I have only used fabric softener sheets for needle-turn applique so I'll be watching for other responses. Oh, and I use used dryer sheets--not new ones.