Hi. This is a great idea. The following is not a criticism, please note that, but a reflection of how I have come to see your story.
One thing very evident by your writing style here, is that it is quite explicit. From the summary, you set out to do something and in the actual chapter, in every paragraph that follows, you are true to the purpose and Sirius's character in the way you are writing him is revealing and fitting. The way you have written it head first, it reads as a standalone chapter rather than as part of a story until maybe the last paragraph. This is merely an observation. The line: Somehow, he never could twist his lean face into anything approaching the jowly countenance of their Potions Master for instance, is where I found myself smiling and thinking, so true, but I'd have never thought about it exactly like that. Even though it breaks my heart to think what it really implies about Sirius here in the moment, hats off to a great description.
I have a feeling that to counter the truth about Sirius you will play with here, I'd have to frequently go back for consolation to what Jo wrote about his picture with the Potters on their wedding and how it transformed his face. Ah, what an indulgent story yours is going to be :)
My favourite paragraph is where James reconsiders throwing the jar. Bravo! It ends on such a sad note, which was lovely.
I have enjoyed this story and would certainly look out for it. One thing I'd suggest is simply to not make Sirius too aggressive. I'm going to make a connection here to how chronologically, Jo first introduces 11 year old Sirius in the books. Remember that? So he's always been the rebel. The nastiness I think is bound to have emerged when his odds with his family became far too intolerable to ignore. Given where your story is situated, the Sirius you describe is quite on the money actually. I just wish somewhere you'd show before the end that his redeeming quality is one that would have been developed as a result of the time he spent being his best friend's "twin".
Looking forward to more :)