My process probably takes too long, but I trim a pretty good amount of the fat first. I take each section individually, trim any fat, and give it a very coarse chop (1.5" by 1.5" or so).
I prefer plastic food service gloves and a cleaver when it comes to trimming fat. I can feel it with my hands and I can separate larger sections quickly with a cleaver.
Trimming does take me longer, but, for me, the coarse-chopping with a cleaver saves a lot of over hand-pulling with pvc/insulated gloves. I find hand pulling to be a little tedious. A few whacks with a cleaver, and boom, I've immediately got the consistency I want.
Three 22.5" OTS's, 18" OTS, SJ ,Custom Trailer Cabinet Smoker