I dropped the jacks and manhandled the TC straight by playing jack games. My Happijacks weren't very happy, so we did it manually. Took longer than it should have, but it's currently straight within 1/4" at the front. I messed up and the back is touching on the other side (3/4" total gap, so it doesn't take much).
I'll look into blocking and perhaps switch over to plywood and guides. The TC is a NL so I don't know if the fiberglass bottom is causing easy slipping compared to other models. It seems to sink a litle into the mat, so I assumed all would be good.