I would put a plain border on each of them and bat and bind them each to make 2 quilts.
Then you have 2 quilts for your family heirlooms.
I wouldn't worry about whether to do machine or hand quilting. I would do machine to reinforce the already there stitching.
I think that this method would help preserve them and by using new materials it would help to strengthen them as well.
Hope this helps.
Kirsten