Finished! Thank you all for your advice on that final border. I ended up removing, ironing it, and reattaching it. Each border turned out to be about 3/4" too long in total. I had been so worried about the corners "flaring out" that I overcompensated on my mitered-corners, making the quilt a tiny bit circular rather than a perfect square. I blocked it before attaching the binding.
When I asked my original question I had already "stay stiched" just inside the black border. When I reattached the border it ended up looking okay on the back because there was already a line of stitching there. As predicted, I created a couple of folds on the back but was able to limit it to the first border I quilted (I was more careful with the others). If I make a long label I can cover the trouble spots! But since I tried something new with each border on this quilt, I may leave the puckers on the back to remind me of the lesson learned.
I've attached a photo detailing one of the corners to show how nice my story ends! I'll put a full picture up in the quilt gallery.
Thanks again for your advice.