Yup! I'm insane, I know!
I considered that solution, but the "cush" of that fabric makes it so shifty that I can't even pick it up without it moving right across and becoming misaligned again. It's hard to explain, but knowing my machines and my operation, it wouldn't be a great fix. Also, the columns are already pieced and they are not coming back apart! Essentially, I gave up and just tried to match the other squares as best as I could and write those off.
The main thing I'm looking at right now is the best way to trim the edges to make them flush again. Then, I can only assume that I'll make sure all of the seams are pressed flat and try to match them up when I sew the columns together, and use an insane amount of pins to hold each seam to the one it's supposed to be aligned with.