Fred! You are the man!
I was looking at your home dojo pictures just last night...how ironic.
I would have thought wrapping the cover over the cut would help keep it looking good; guess not.
Next question: with what to cut? Big utility knife? Circular saw? Light saber?
Nick, there's always room for improvement of somebody else's method.
If you're concerned about a clean corner and want the cover to wrap, then cut from the underside. (Be careful not to reverse your guide pattern) Don't cut quite all the way through (if you use an extendible snap-blade knife, you can control the depth of the cut by setting the length of the blade) but overlap the two cuts on the inside corner. Snap the foam along the cut and peel the foam off the vinyl cover.
What works really, really well (if a) you're not concerned about cutting through the vinyl and b) you have a way to raise the tatami off the floor while it's being cut) is a stainless steel serrated bread knife. Otherwise, I'd go with a snap-blade utility knife, the wider the blade the better.