"We could do physical Code Review sessions, but it's difficult because I've a very chaotic schedule"

Aren't you a developer? You're not a manager? Can you explain why you have a chaotic schedule? If you don't code, why are you doing code reviews then?

Seems like that's the fundamental problem right there. You said so yourself, physical code reviews would solve it. So that's the solution, the problem is your schedule, fix your schedule.

You're making this person accommodate your schedule(in addition to their own), because you don't want to do your job. Again, unless I'm missing something.