Akira does not take kindly to people Touching His Stuff. At all... There's a previous mini-arc about exactly how much he really doesn't like people Touching His Stuff.
The girl is incidental. The Baddies were dead meat the moment they raided Gang HQ.
I mostly agree with you. The trigger was these arseholes going in to Gang HQ and kidnapping Sheryl.
However, I doubt Akira would have gone to this extreme for anybody else in the gang, and I think that's the nuance you are ignoring.
When his wallet was stolen, he chased the girl until he got his wallet back. He was willing to fight others to make her pay, but once his stuff was returned, he said "meh" and moved on.
When he was in the ruins with other hunters, he wanted to avoid as much conflict as possible because he doesn't like risking his life just for anything. And we have seen plenty of times in the past where he aids others, just because they happen to be nearby, not because he really wants to do that.
Here you see an Akira that prepared to destroy his property (vehicle) to avoid a prolonged confrontation and fight to save Sheryl, heal her and then make them pay.
It is not the gang he cares about, it is Sheryl. She is his property (if we want to give it the same perspective you imply) and they touched her.