maybe try pinning every inch or so to hold it in place?
it is a unique problem since we normally want the (machine bed) to be smooth/slippery to enable us to move the fabric freely when quilting- dealing with bulk-
if you pin every couple inches and remove the pins as you come to them it should hold everything nice and straight-if holding it with your fingers does not do it for you. i would be hesitant to add anything to the machine- unless you can remove it again.