Singer is definitively pro-abortion, for basically the reasons I mentioned. It's not terribly nuanced, it follows pretty directly from his basic ideas.
https://en.wikipedia.org/wiki/Peter_Singer#Abortion.2C_eutha...
I'm not super expert about it either (at best a casual armchair philosopher), but from what I know Singers philosophy isn't specifically about suffering, it's about weighing interests. He assumes that the desire to avoid pain is one of the more important interests, hence it takes priority most (but not all) of the time. It's not black and white, it's more of a calculus about weighing the different competing interests of individuals, with certain classes of interests being given more weight than others.
I think Singers arguments in favor of abortion actually go farther than what OP's post implied regarding the fetus' capacity to feel pain. Singer argues that a fetus is unable to have any self-interests (including the desire to avoid pain), hence the interests of the mother should be given priority. I think this is taking it too far myself; I can agree with the delineation of the fetus' capacity to feel pain, but it is not clear to me at what point (if any) Singer feels it would be immoral to abort a fetus.