I seriously have a problem thinking outside the box sometimes!
Thank you to those that said they machine stitch to the BACK and wrap to the front!
I can't seem to "get" binding just yet, and have flubbed up 2 because they're obviously not done properly (on the corners), and I somehow didn't have enough fabric in spots (even after trimming the batting) to pull completely around and cover the attaching stitch line. When I (machine stitched) the wrapped part, it just got all wonky and looked HORRIBLE in the spots that I had trouble with all the way around, and the binding wasn't even matched up evenly front & back.
Long story even longer...
I'm going to try a wider binding strip (2.5") next time and see how that works out.
(btw, machine stitch both sides (SUCCESSFULLY!) is how I ultimately want binding to happen.