I’m assuming this is a split unit? I don’t have one, but I thought there was a float protection to prevent the AC from running if there was too mich water in it. Of course, this would probably only work if the clog was near the unit itself.
“Gunk” is probably a combination of algae sludge plus any captured lint from the ventilation. Not much to do about the algae other than blast it with a disinfectant like bleach once in a while.
How’s the incoming air filtration into the unit? Is it sealed reasonably well at the filter?