It's not cheating to use the machine to sew the front OR the back - whichever way will get it done the best is the way to use.
The main thing is to get them done and have them be neat and sturdy.
It's not cheating to pull the back around to the front, either. If the backing coordinates nicely with the front, it's a great shortcut. I have only done this a couple of times, but when I do, I try to double the thickness of fabric that protects the edge of the quilt. Mitering the corner is tricky but it can be done. And if you don't want to fuss with it that much, use an Amish-style corner and it will be attractive, too.
Whatever gets them done - do it. Even if you have to do it by hiring (or bribing with chocolate) someone else to do it for you.
