Wanted to post something a little more put together, as the Mullet drabble is clearly a work in progress.
Sirius broke out of prison to get revenge on Peter and not to raise Harry because, by the time he had figured out how to break out, he had decided that he was too broken of a man to raise Harry. That, paired with the insanity from the Dementors and the guilt for not being a better friend, channels into James and Lily's voices, yelling at Sirius. Only when he started listening, they were yelling about getting his head out of his ass. But what they didn't know, because he had betrayed the trust they put in him by choosing a rat and now they were dead, was that Sirius has always known that there's an intense, dark, black side to him. Hence, he knew that no matter how broken he was, he could at least still get revenge on Peter. A tiny part of him hoped that once he was away from the dementor's influence, maybe he could fix himself up or at least be good enough so that he could not raise Harry but be Harry's life.
Sirius's Plan:
Gets the paper for the crosswords (he was trying his damnedest to be a normal fucking person, and by Jove, it worked)
Test the theory about dogs being less affected by the dementors up close and personal, which meant antagonizing them and seeing how much of his soul got sucked out as Padfoot.
Slip through the bars because, damn, is he starved
Daring escape scene where he hides from dementors and guards alike. Action movie style.
The shift change comes in on the boat as apparition can be hard when you've been using a lot of magic to sustain a patronus and have been around dementors for an extended period of time. Sirius recons they can have someone less tired apparate to land to get them a new boat. At least, that was the plan. Till he circled the island twice but couldn't find a sign of the bloody boat. He started swimming, had to avoid the incoming shift change, and eventually returned to land. Unfortunately for him, he is so fucking stoked to see land and just lies down and rejoices for a min and fucking breaths; he gets spotted by a watch guard who tries to chase Sirius down. Cursing himself for acting so foolishly, how could he get distracted by something so bloody stupid as land at a time like this? He managed to give the guard the slip in a nearby wood, shifted, and made his true escape to anywhere but there.
Suddenly there is a niggle of not being quite as alone, of feeling seen, understood, and of knowing that she was alive. Following the pull kept Sirius going through the night and well into the morning when he collapsed from exhaustion as Padfoot tried to keep away from any Aurors, cops, or animal control while also needing to be with her again. (Hermione is reading the breaking edition of Daily Prophet, which is alerting the wizarding world to his escape and having some pulls of her own.) Once he wakes, the pull is gone, other than a few faint flickers here and there less and less often throughout the day. He knew he wasn't crazy all those years ago when she was gone, but he could still feel her. He knew she was still with him now. Now, Sirius just had to find the rat who caused his life to go to utter and complete shite rather than just run-of-the-mill poopy, turn him into Moody, the only one Sirius has a chance of convincing, clear his name, and get his girl, his pup, and his last remaining best friend back together and under one roof.
When the bond stops flickering and goes back to a steady low buzz in the back of his brain, Sirius is finally able to get his wits about him enough to figure out where he is. His brain still isn't too good at keeping focus, like a moth to flame, drawn to what feels good. And the bond activating feels so good it blocks everything else out. He remembers running through a forest for a while and then through some fields. He's currently curled in an alleyway on top of crushed, soggy boxes. Deciding he was awake enough to stop suffering the piss smell that seemed to overwhelm every alleyway in Britain, he got up, had a stretch, shook himself off, feeling his skin shake away from his bones like the dog he had been for so long, not enough fat or muscle to hold it all in place, and promises to nick himself a sausage roll, and went to have a look at where he ended up. It seemed he was on the edge of a city and suburbia; up the hill seemed to be row housing broken up by trendy shops, and down the hill and round the bend, the city seemed to be picking up a bit more, with a large graffiti piece about some bloke who wasn't a fan of Tescos across the street from him, which was a grocery shop if he remembered rightly. He assumed it was a happy memory as it was hidden behind a cloud of fog and cold in his mind.
Not seeing a lot of dogs about, he aimed away from the city he wanted to see more of; any place that lets you draw on the walls has to be worth visiting, as a human. He chose the residential area, hoping to find a park to steal a bit of a picnic or get a snack from a child in the mood to share with a big but sweet dog. Sirius spends the day not having a ton of luck and eventually finds himself at Magnolia Crescent after having to hide in some bushes after legging it when some bloke looking related to a walrus tried to shoo him out of the neighbourhood; he did not just escape Azkaban to get bossed around by some fat, balding, middle-aged, moustache clearly compensating, git. Sirius finds a nice secluded area between a garage and a fence and naps. Sirius wakes with a bang, seeing some kid loosing his shit on his trunk till he regains a moment of composure. Wait, trunk? Sirius walks out of the shadows to get a better look at this magical kid and sees a mini James. Sirius internally is losing his shit, but externally is frozen. Mini James notices him and raises his wand and Sirius can't help it, he lets out the smallest of warning growls, demanding the demons playing tricks on him leave, till mini James calls the knight bus, and Sirius takes off running to Hogwarts.