Greetings. I love all the suggestions and they are what I do when trying to flatten a wavy border on a quilt before trying to topstitch it on a longarm.
What I often try to mention is the reason for the waves. Usually it is that a border has been added to the outside of the quilt without measuring the interior of the quilt and applying the border to that measurement easing in the excess.
I often take off these outer borders and shorten them easing in the excess there. It's easier to do that than to flatten an extremely wavy border.
Other times the waves are caused by bias and you'll see that a lot in quilts placed on point. Often times the only remedy for an on point wavy quilt is to add extra borders and ease in the edges.
If the waves aren't too extreme the steaming can help a great deal as well as hand basting the edges and pulling in your excess. Often times just using a very long stitch on you machine and sewing 1/4" in from the edge will bring the waves in enough to quilt out your excess once you are quilting your top. If you measure the interior length of your quilt top and then measure the outer edge of your border you'll see just how much you have to ease in. I've had them with 3" excess...those were the ones I redid the borders on :).
Are you quilting it on a frame or in hoops. Hoops and a thicker batting can do wonders. Good luck :).