This *might* work -
Are you familiar with the term "easing in" fabric when joining two pieces of fabric together? It's basically getting a slightly longer piece to lay fairly flatly against a slightly shorter piece - either by stretching the bottom piece while sewing the seam together or by distributing the extra fullness of the longer piece into a very slight gather instead of a pleat. This is often done with set-in sleeves.
Anyway -
You could try unsewing the quilting between the crossing lines - then - from the back side - try redistributing the fullness between the crossing lines.
Resew from the back. You would end up with a bit of "puffiness" - but that might be more tolerable than the "pleats".
There would be the issue of reburying the sewing ends, but that might be more tolerable than a complete redo.