IMO, a (very) thin batting (like a layer of thin fleece) can actually help with the tipping glass issue, as it gives a spot for a lumpy seam junction to press down into.
I would say either use a very thin batting (or use fleece as the backing, perhaps?); or make sure to flatten (open, furl) your seam junctions as much as you possibly can.
I don't have a quilted tablecloth, but I do have a few quilted placemats; I used Insulbrite inside of those and they're very flat - nothing is even slightly tippy on them. I did pretty dense FMQ over them, which I think helps with the flatness too.