Next time, try Elmer's glue dots down your seams, iron them dry and sew. This should help on the border seams, sometimes, even pinning, you still get puckers and pleats...I found glue stick or dots works for me. Also, if you glue, then you are not pulling at your fabrics as you sew them together.

I was helping a friend put a quilt on a frame and we ran into the same problem. No way could we get it to lay flat. She had to take off the borders, measure the quilt again for each border and resew. It will be worth taking all the borders off and trying again. Make sure your panel is square (or rectangle) and then measure and cut the borders as necessary. You will have to measure each border before reattaching.

Your long arm quilter, if it only has a "bump" on one border, may agree to take a tiny pleat/tuck in the border when she's doing the quilting. Whether you will be satisfied is the question-I would probably detach the border and re-measure if I caught it before putting on the long arm frame.

How did you sew the borders on? the sides frist and then the top and bottom? or did you go round the the panel e.g bottom, side, top and the other side?

With my panel quilts, after squaring/even up, I measure thru the center of the panel and that is what I cut the border. It works for either way, Whether you do the sides first or the top. then continue to do the same as each border is added.