When I did the actual quilting I treated these like it was one whole quilt top. I did not stop and start on each placemat. This was a way cool technique that I used. I know lots of other quilters do this all the time, but this was my first, so I kind of winged it and figured it as I went along. The end result turned out great.
I'm not sure where I found the suggestion to setup my end clamps like this (might be Sharon Schambers) but the fabric extensions make it so much nicer. No more clamps getting in the way. Using corsage pins gives me good solid connection and I use 7 pins on each end. The material I used was a heavier denim weight fabric that was hanging out in my stash. I made a sleeve to slide a dowel in for the clamps to grab onto, and a wide seam on the pin edge making it a half inch wide, 4 layer edge for the pins. After I used these extensions for a while, I found the dowel would slide so I had my husband put a staple in the middle.