I don't see the issue.

Mooch only triggers when you pull up a HQ fish you can mooch with.

Mooch II only triggers when you pull up a NQ fish you could have mooched had it been HQ.
If Mooch II is on cooldown at this point, you don't get to use it, the end. You re-cast your line just like before you had Mooch II.

What interference could there even be?

I think you're mistaking Mooch II triggering as you catching something HQ you could have Mooched with.