The beautiful Twister quilt I've been working presented this challenge, above, because the pattern is very bias-y.
The way Twister blocks are cut and pieced causes the finished piece to be very stretchy. So when the borders are added, they are tighter than the center. Every Twister quilt I've quilted here in my studio does this. So I've learned to do the "lining-up" trick to keep it rolling smoothly to the end.
First, I make sure there is a nice horizontal seam line, and I line it up on the roller:
With my hands I work all that extra fabric above the seam line into the quilting area. Then I lay my iron down across every square inch, steaming and then lifting and moving to the next area. I don't run the iron on it like when I'm ironing a shirt. I just press, steam, lift, and move to the next area. Eventually it looks like this, and the seam line is still in the same spot:
After it was quilted, it looked like this:
When I got to the end of the center of the quilt, I still had this much extra fabric that wanted to be worked in:
I did the press-steam-lift treatment - keeping a horizontal seam line on the roller - and it laid down nice and flat:
This picture, below, shows where all the extra fabric went. You can see how each Twister block is holding a little extra fabric. But at least it is holding it evenly, and that's the goal:
The quilting sucked in all of the extra fabric as well, and now that I'm done with the center, the borders are nice and flat and ready to be finished off: