I dont' know quite what to say to this amazing comment. First, I am very flattered by your compliments. I am pleased you enjoyed this so much. Secondly, we are of the same mind on so many things here. Albus is the third character in this story (IMO) and his hand plays a big part. Sirius can't forget Halloween 1981. Everything leading up to it, everything after it. I think he is still so completely torn up about the Secret Keeper thing blowing up in their oh-so-clever faces that he sticks with Albus because he thinks it's their best shot. Except Sirius is never a company man so there are streaks of rebellion that are ever present. I do love to think what if Sirius could say "fuck this" and take Harry go. But I don't think he could have done it. I do think in the background, even in canon, Dumbledore is turning the screws on Sirius. About doing what is best for Harry and protecting Harry. It's too big a risk for even Sirius.
Sorry a bit tl;dr. But yes he wants to trust Albus cause he has nowhere else to turn and lives in the past so can't move forward.