Oh, I feel your pain! I am currently in the process of "unquilting" a throw for my MIL, which was a Christmas present that didn't get finished in time so I have kept it to get it donel Since I don't have that deadline, I decided to take out the quilting from the last block that I did get done because it was so puckered and the stitching looked awful. Well, in the process, I decided I needed to remove the STID around the inner border so I could smooth out the block. On thing lead to another, and now I am taking all the quilting out and am going to start that over.
The blocks themselves look good, if I do say so myself. The two borders are fine, even matched the stripes at the mitered corners. However, the quilting - well, not so much! My DH did build a shelf above my cutting table and put the (new) TV up there (it formerly sat n the corner of the table) and installed a pegboard over the table so now there's nothing at all on the cutting table and I can move it away from the wall so I can lay the quilt on it and let it drape over the sides and not have to bunch it up. Once I get all the stitching out (I had done about half of it), I think it's going to be so much easier.
I plan to use binder clips to hold the backing, the batting smooth and flat. Then I'll pin the center block, stitch it, move to another middle block, stitch it, etc., returning to the cutting table to smooth and pin a little at a time. This is the biggest quilt I have done so I'm learning you can't do a quick pinning and expect it to all stay nice and smooth and flat!
I wish you luck and hope you feel more encouraged to finish it soon.