In fact, with him calling Babs right afterwards, I would think Babs would be more likely to be someone's avatar.
I agree with that. In fact, if I had to pick one female character who I think might be the closest to being Devin Grayson's self-insert/Mary Sue, I'd say Babs hands down.
after repeatedly hitting rock-bottom, he was supposed to be happy and flying high again. Unfortunately, we had to wait all the way until Tomasi's run
To be fair to that annual, it ended on the idea that Dick needed to find who he was so he'd be happy with himself, so Andreyko didn't get everything wrong.