I use spray baste for all of the quilts I quilt myself. Lift off the back in the area where you are finding wrinkles. Reposition and smooth out the wrinkles with your hand. The baste should reattach If you need, do a light respray of your baste. I also use a large 12.5 square as a press tool. I start at the center of the top or the back and firmly push the template toward the edge where ever I see small bumps. This will usually smooth them out easily. Don't give up on spray baste. Keep trying. I get FAR fewer wrinkles during quilting when I use spray baste than when I used pins.
(I am not sure about spraying water on your piece. That might lead to unexpected shrinking of your fabric. Just gently separate the back from the batting in the area you need to.)