I glue-baste my quilts up on a folding table. No tape, no pins. It's quick, and easy on the back and knees! I can even do parts of it from a rolling chair if I'm having a bad back day. Gravity does some of the work, the glue does the rest.
I will never baste a quilt on the floor again!
I've always struggled with birthed quilts so I stopped doing them. I always had something baggy, somewhere - but maybe I just wasn't very good at that method. I like Geri B's suggestion to have the backing just a titch smaller than necessary, that might have helped me. Although sometimes the bagginess was on the top, so maybe not!
When I did a birthed quilt, after sewing the edges together (before flipping it) I'd take my applique scissors and trim excess batting away right up to the seam to help make the edges less bulky. Time-consuming, but made the edges look a lot better IMO. If you're thinking of adding binding, this would help reduce some bulk, too.
There's really no "wrong" way - I don't think I'd ever do what you're talking about but that's absolutely not a reason why you shouldn't run with your idea! I think it's great you're experimenting, and maybe you'll come up with a style that is uniquely your own.