I would take the measurements from the center and re-cut the borders to those center measurements.
You can ease an inch or more of either border or quilt into three or four feet of quilt.
If the quilt side that you're sewing is longer than the border, put the quilt next to the feed dogs and keep a little tension on the edge as you sew it. If the border is longer than the side that you're sewing, put the border next to the feed dogs and keep a little tension on it.
When you get the top onto the frame, you're going to have some places where the top is blistered up. If you can mist those blisters with water, it might draw up some of the excess fabric. It's going to take some careful work in those bubbled-up areas, but they won't be as obvious once the quilt is washed and dried. If you can use an allover design that's open, (curls rather than closed loops) that will help you disguise the problem even more. A fusible batt can help you beat the top into submission, too.
I don't have a long-arm - I have to use these tricks in free-motion quilting. I've bought some really unbelieveably wonky vintage tops on eBay. One of them made me cry when I laid it out to sandwich it. Such a pretty top, but ohmigosh, it was awful. It was a Drunkard's Path that had been pieced by at least two people. One knew what she was doing and the other one didn't.
The blocks were trapezoids, not squares and the quilt was not square anywhere. That's probably why it was a UFO - she probably took it out every few years and remembered how awful it was and put it right back into the linen closet.
I ended up putting two allover designs on it, quilting heavily in areas that needed taking up and leaving more room where the quilt was flat. Once I got it laundered, it was quite pretty, but mercy, it took a lot to get there!
Good luck to you!