I use both hands for basting or hand quilting and suggest you use a strip of fabric and stabilize the injured finger to the last two of your hand to keep them together. Then use your thumb and first finger to hold a needle and use this hand under the quilt to push up the needle for basting or stitching. The left hand is not as agile but you can see where to put it, catch it with your right thumb and finger and push it back up. Might be slow at first but you will find it works.
Carol J.