I don't know if I dare write this. You can delete it if you wish, but I PULL on both sides of the needle. Yes, I do!
If one side is longer than the other, I put a pin on the seams that need to match (if you don't, the seams can "pop"). Then I put one hand behind the needle and the other in front, and pull apart as it goes under the needle. The fabric still goes where the feed dogs want it to. Just feed as fast as they want it.
On borders that are not quite the same length as the quilt, I put pins at both ends, in the center, and then in several places between ends and center, always finding the center of the space that is left. (I fold it in half to find centers.) Then just a gentle pull as I sew gets it perfect. I can get rid of a lot more than an inch that way and it can't be seen.