I'm much the same, Ross. I got my 1st muscle-up a month or two ago. I am struggling to get 15 dead-hang pullups (maybe on a good day) and I'd definitely struggle with 15 consecutive full ROM ring dips.
You do obviously need to have a certain amount of strength to perform a muscle-up; you certainly need to be able to perform a full ROM pullup and dip and at least a few reps of each I would think.
After working muscle-ups for a while (trying to introduce less kip), I'm finding that determination (this is extremeley under-rated) and skill are far more important than strength.