So after more research and reading, I will not be taking it apart! First off, more work than I need. The handquilting is fine, it's the embroidery. I just bought a bunch of embroidery floss to match the quilt. That part is done!
My first step is going to begin tonight - I'm going to take out some of the embroidery of the bottom of the basket (it's all bunched up there).
Next step will be to hoop it, and mark it with pencil so I can follow the pattern, and do the hand embroidery piece by piece.
Once all of the embroidery is done, I will cut off the pieces of the backing and put a piece of fusible interface between the two (just a narrow strip) to hold them together.
Next step will be to add a backing, and then hand sew every 6-8 inches following the cross hatch hand stitching that my grandmother did ... and final step will be the border ...
I see lots of long summer evenings in the gazebo working on this!
Thanks for all the tips!