Jump-ins are a different problem than cross-overs. The hit-boxes on aerial attacks in general are kind of goofy to me. Because of that, you get some opportunities on cross-overs to land something like s1 or d1. But then set up your AI to JIP and try to beat it clean with s1. A lot of times, it's all you can do just to get a trade. I'm not convinced on back-dashes. The vast majority of the time I've tried to use the invincibility properties of back-dash, it doesn't seem to matter much. I end up getting caught on the tail end of an attack or from the following multiple hits of a move/string. Then you can't break.
I haven't worked on it, but the idea of running underneath a jump-in and whiff punishing might be the proper option. Although, even if it is, I can't see it being universal. Some characters like KL or KJ don't have to be as deep to initiate their JIP's, so maybe you get smacked for trying to run through. I don't know.