I mostly use a hoop to hand quilt but not always. I think I would find a frame difficult because I just wiggle around too much to get comfortable when I'm quilting (or any other time for that matter). My suggestion would be if the puckering is not horrible, leave it as it is. Otherwise I think your only option would be to rip and redo and that may end up being most of the quilt. If you used a cotton batting, your quilt will pucker in the washing/drying process and those areas on the back will probably not be noticeable.
When sandwiching, I use my cutting table and larger binder/bulldog clips to get all the layers as taut as possible. Depending on the size of the quilt, I will either pin or thread baste. In either case, I pin/thread about a hand-width apart in both directions beginning in the center of the quilt. Don't usually have many issues with puckering. I do find it important, however, (lessons learned) to check both sides of the sandwich as I quilt for smoothness as I go along.
Perhaps you have a hoop that is just too large for you? I use the cheapies from JAF. Perhaps try a smaller one and see if that makes things easier for you?