Hi,
Well, I speak from experience...I have several quilt tops that I "inherited", the ones that were so special to me, I tried to keep "as is" and work with them, if possible. I actually have a grandmother's flower garden, parts of it were not as well sewn...I ended up tying it rather than quilting it..and, it actually turned out pretty good...
On the other hand, I have a lone star, there was no way to make it work, there were actually too many diamonds as it got to the center, and it made a huge lump...so, I had to carefully take it out and am trying to make it work...I think it is really just up to you...I know you said you are more of a "machine gal". Do you have a friend or someone you trust that is more a "hand sew" person that maybe they can help you?..Just a thought..
Good luck!
Kif