That sounds like a basting problem, then, rather than a quilting problem. How are you basting, apart from on a table? If you can sort out the problem through your basting, I think that'd be hugely easier and quicker than what you're proposing. How big is the quilt?
I probably make more fuss basting than the vast majority of people, so take this with a pinch of salt, but here's what I do anyway.
1. Clear enough floor space and make sure it's clean and dust-free, including in the hall so that I can get to the loo without trekking dust or hair onto the quilt. Prepare the top, backing and batting, and make sure I have everything I need within reach (since I have to shove the dining table into a place that blocks my sewing desk).
2. Put the backing on the floor, smooth it out, make sure it's straight, get someone else to help me hold it taut, and then tape it down around the edges with masking tape. If you have a carpet, use pins instead.
3. Put down the batting, smooth it out, put down the top, smooth it out.
4. Crawl around on the floor with big safety pins, putting about one every 12" and more frequently around the edge.
5. Take off the masking tape. I leave the next part for the next day as I have severe ME/CFIDS, but you may want to go straight on. If not, fold up the quilt carefully.
6. Put the quilt out on the dining table, making sure I smooth out anything that's got rucked up from having it folded up overnight.
7. Thread baste using herringbone basting stitches, about 3" apart and closer for the outside row. I use Sharon Schamber's technique for the herringbone basting, you can find the video easily on YouTube. I do two backstitches at the start and end of every thread.
8. Take out the safety pins and we're ready to go!
It's time consuming, but on the other hand I have never in my life had anything other than beautifully flat quilts as a result, with no puckering or anything of that nature. I also rather like the thread basting process, it's easy and peaceful.
When I had to do a quilt that was larger than the floor, I did it in two sections with a friend. We taped three sides, and on the fourth we weighted it down with stacks of books. Not the easiest, and I wouldn't want to do it again, but thankfully it worked the first time around, we didn't have to redo anything. That quilt was about 89" square finished, it's the largest I've done.