I treat it like cleaning the trim around windows.
Spray a spray cleaner. Doesn’t have to drown it - just get every moldy surface wet. Bleach solution is great (don’t get it on you). Windex is pretty effective, too.
Let it sit for a few minutes to soften everything up, then get in there with cotton swabs and paper towels.
It seems daunting, but that first paper towel and swab are going to already remove like 80% of the filth, and the rest after that is just detail work for as long as you can stand it.