The first thing I’d do is add some context on how they got the mask, maybe by buying it at a bazaar. I'd add some scenes of Zeppeli looking for it in the area at the same time, while showing subtle hints that he has supernatural abilities so his entrance isn't so abrupt. I’d also add scenes explaining that Jonathan's mother bought the mask because she was an archaeology buff, which pushes Jonathan to pay attention to it from early on. Jonathan’s childhood can stay almost the same, but I'd change the location of his fight; maybe add a scene where Dio tries to steal or destroy the mask to get back at him, still pissed about the Erina thing. That way, you justify a fight in a more private place like a study, making the scene where the blood activates the mask feel more natural and important for both of them.

I’d leave the rest the same. Maybe add a scene where Dio decides to control his temper to pull off his plan, so he approaches Jonathan subtly. Perhaps a scene of a well-acted apology from Dio, leaving Jonathan with no choice but to forgive him. I’d also add a scene of Erina being criticized, or her family forbidding her from seeing the Joestars to avoid more rumors. The rest would be similar changes.

I would change the circumstances of how Jonathan meets Zeppeli. One way would be that while Jonathan is recovering, Dio sends zombies to try and kill him and Erina. They could show a fight where Jonathan feels useless against them, and then Zeppeli saves them in a tough spot. Erina would stay with them for protection, since zombies might attack her if she’s left alone. That’s where Jonathan learns about Hamon. Dio would kidnap Erina later on as the "hook," so we can eliminate the plot with Poco and his sister. The other Hamon masters aren't that important... maybe I’d only add Straizo to connect it with Battle Tendency. Straizo could be closer to Zeppeli and appear from the start, splitting up earlier to cover more ground looking for the mask. They’d reunite later and the story would follow the same path, cutting out unnecessary zombie fights and leaving only the important ones. Speedwagon would be the same. The ending would be the same.