Here's an idea that works for me. I haven't pieced a quilt, but I HAVE had to press the seam on the backing.
I never press the backings before I lay them on the machine, I use a STEAMER. I found a steamer at a garage sale. It's one you can tip forward (friend bought one that dumps the water when tipping -- ugh). When I have a quilt back that's been pieced, I run the steamer across holding with one hand, and holding the seam apart with the other....
never burned myself either. Works great for that! I suggest it for all the people I've taught. Beats pressing a 108" wide backing!!!! But it would work on the QAYG quilts.