I have had the same problem, but lived to conquer it and now love spray basting or glue basting. Of course, by the time you peel it all apart you will look like a white fur ball. I know this from experience.
I like to lay the batting down on my table. I clamp it down all around the edges with my big clamps. (They came in a cheapie set from Walmart and look like chip bag clips.) Next, I smooth the backing over the batting and clamp one edge and half of one end. Flip the unclamp half of the batting back and spray baste. Repeat for the other half.
Flip the whole mess over and repeat for the top. Somehow, for me, starting with the batting on the table makes things lay still. Every time I put the backing on the table and add the batting I get wrinkles.