There is no API to get “channels I am a mod in”
You will require a uservoice to request this functionality.
https://twitch.uservoice.com/forums/310213-developers
You would be better off reporting the account rather than cross banning.
This sort of accounts are “fire and forget” and generally in my observations by the time you’ve banned them in channel 1 they already hit channel 2/3/4/5 or don’t bother trying due to their fire and forget natrue.
So this sort of defence generally doesn’t work in my opinion.