No, you are not cheating. I have a quilt made by my grandmother back in the 40's. It has the backing folded over to the front for binding. (She used a good cotton for the backing so the binding has held up okay.)
My quilt is getting a little worn but I still love it. I have seen other quilts that my grandmother made and some of them have the regular binding on them. My grandmother was a very smart lady and if she thought it was okay to do it, then it was okay.
Tying the quilt is okay too. My mother and grandmother have done it both ways. Some of their quilts were tied and some were quilted. (My grandmother quilted most of hers, but that was in the day when a group of her friends would come over; they would drop the quilting frame from the ceiling and all of them would sit around the frame and talk while they were quilting.....or maybe they quilted as they talked... :)
I have an idea that the quilting was just an excuse to get together. Gee....if I had that type of quilting support, I would quilt it too.
In later years, my grandmother tied several of her quilts because her friends had gotten ill or had died...(she lived until she was 95).
Your quilting style is just fine and don't worry about the quilt police. Enjoy yourself. :thumbup: