I have a cheap cutting table from Joanns that is less than an inch thick.
You can buy slip on plastic clips to hold the quilt tight. I got mine at Quilt in a Day online.
It has made a big difference.
You can also use the black office clips but they are bulkey. But really cheap at the dollar store. I use the plastic clips for the backing then use the black clips for the top.
No more folds or kisses.
I also move my larger quilts and do the middle first then move to each side and clip and pin. The table is only 36 inchs wide so have to move the quilt to get it all pinned.
I also have a machine with a 10 inch throat and that makes all the difference in the world when quilting.