As an update, I wrestled with my setup all afternoon yesterday. Keeping in mind what Tartan said about the walking foot doing the pushing, I increased its pressure and readjusted the tensions. I put a fat book into the trough to the left of the extension table, and it made a noticeable difference. But alas, I was still getting uneven-sized stitches (nicely made but uneven) because of the pushing I was doing to move the quilt (pushing too much makes them smaller). This was particularly annoying because the quilting lines were in a show-off spot. I redid a bunch of them.
Then I looked suspiciously at the place where the quilt slid off the extension table in back. I had thought that this wasn't a problem, since it was sliding downhill and had a big place to go. Plus, that was the same direction it needed to be going. So I moved around to the side of the table and pushed the quilt with one finger. It slid easily. At that point, with neck and shoulders hurting, I was ready to take the extension table outside and smash it on the driveway. And I am not a tantrum-throwing person.
I had thought that if other people used the extension tables to quilt, I could, too. But now, either DH will need to find a way to cut into that butcherblock, or I will be buying foam sheets and rewatching Prism's videos. Thanks to all of you who reached out to help. You're the greatest.
Hugs,
Charlotte