I have a couple of thoughts...
If you tear it out back to where the problem started, will it change it enough that the following borders will still fit? Could the blocks in them have been "tweaked" to make them fit?
Without seeing the quilt, can you make a row of "wonky" style blocks or an applique of some kind, in the border that would camoflauge you straightening it up on your round?
Can you post a picture here so we can be of more help?