First I would block the quilt. For this amount of distortion, I'm not sure dampening will be enough. I would probably rinse it and spin it out in the washing machine. There may be a demo of how to block a quilt on Youtube.
Before blocking, I would probably spray starch both sides a few times (maybe outside, where overspray won't hurt anything).
Once the quilt is blocked and dry, I would add more machine quilting. Machine quilting stabilizes the sandwich so it doesn't distort. Looking at your photos, I'm pretty sure close quilting would have helped prevent this problem. Even though the package says you can quilt inches apart, closer is better. FMQ stippling, especially in the large blocks (but actually everywhere), would help a lot. It takes some practice to master FMQ, though.
I would probably never use wool in a baby quilt just because so many people are allergic to wool, and babies have such delicate skin. Hobbs wool batting is supposed to not shrink; I think they have a patent on a special bonding process for their wool. It's the only kind of wool batting I would ever buy, and then probably only for wall hangings. (It is supposed to puff up very nicely with fine machine quilting, resembling trapunto work.)
Edit: You know, I went back and looked at the photos again. That is really a cute top and backing. Rather than doing all that work to try to "fix" the batting, I myself would just set this quilt next to my favorite tv spot and take out the machine quilting while watching tv. I'd take the entire sandwich apart and re-layer it with a good batting. I'd be a lot more satisfied with the results, I think. Hobbs 80/20 would be a good choice for the new batting; I'm sure you'd be happy with the results from that one.