I would finish it too. Its beautiful!
If you decide to tie it, I would suggest that you put a tie in each corner of each block. I would put the tie ends on the back since the blocks are very brightly colored, or it could get too busy looking. Take a good look at the batting you are going to use to make sure that you can tie it at the size intervals that are needed (ex. every 4-5 inches or more). A cotton-poly blend will probably give you the most flexibility as to the distance that tacking will need to be spaced. Use a pearl cotton or embroidery floss for the ties. Tie with a square knot.
There isn't enough time to find a hand-quilter to quilt it for you before Valentine's Day but you could have it quilted by a long arm quilter. That's not exactly in keeping with a vintage quilt but it may preserve the integrity of the fabrics longer than tying it will.
The important thing is to have the fabrics held down well enough that they won't shift around and rub which would damage the fibers faster. Ties can have the tendency to allow to much shifting if they are spaced too far apart. They can also cause pulling at the places where they are placed and over time that can cause damage to the fabric fibers. It really depends on how you plan to use it in the future. Will it just lay on a bed as an attractive cover but not be slept under? Will it see daily duty? Will you display it in some way? The answers to questions like this should help to lead you in the appropriate direction.
It's really a lovely thing to have. I wish you the best with it.
Rose