I like the idea of having the digital images done professionally. If that's unaffordable, there are a lot of tutorials online about how to do it yourself at home; it's just that this does require a lot of time, the right equipment and materials, a learning curve and, as dunster pointed out, they are not as long-lasting and stable as the professionally done photos.
I think it would be fine to sew new photos over the old ones. I would either hand sew them over the old ones or turn under the edges and machine sew them on over the old photos. I would not take the entire quilt apart -- not worth it! Machine sewing would provide some additional quilting, plus it looks like it would be fairly easy to machine quilt around each photo within the block.
At first I thought you meant you had cut off pieces of ties that had been attached around the edge of the quilt (like prairie points).
Now I realize you mean you cut of the "ties" that were used instead of quilting.
I do think it would add a lot of stability to the quilt if you could machine quilt instead of re-tying. However, your biggest problem will be keeping the layers stable for machine quilting since the edges are already bound and you have no way of inserting basting spray or glue. What I would probably do is first lay out the quilt and pin so all layers are secure. Then I would use water-soluble thread to machine baste the quilt. I would remove the pins, machine sew the new photos over the old photos, then quilt as needed to make the quilt stable. A gentle washing will remove the water-soluble thread.
Or you could remove the stitching around the edge (or simply cut off the edge) which would allow you to layer as usual and attach a regular binding after quilting.