i'm not really sure if your question is about technique or about building wrist strength. in either case, you don't need as much strength as you'd think to pull this off.
everything you've mentioned so far is right. somethings to consider: the bottom arm is the one that really chokes, and the further his face is turned away from the choke, the less it will choke. when you drag your elbow across, use your elbow to point his chin at your choking wrist. if a guy tries to resist it, it will be painful both from the pressure and from the massive gi burn he will give himself. another consideration is proportions; yes, having the thumb in the collar is good, but sometimes the size of the gi or the kind of gi he has will mess it up. it's ok to grab the fabric on his trap without getting a thumb inside, just as long as i can use my elbow to point his chin at the choking hand.
ralek does what i've always heard called "shake the baby." shaking/earthquake motions often allow you to open cracks in people's grips or, in this case, to his neck. then you can slide the choke in deeper. it's one of those things that feel like magic when you do it. all of the sudden you are way deep.
a cool trick to do if the guy has his arms folded tight is to grab the base of his lapel near his waist, pull it up high towards your face, then push it down hard above his shoulder on the same side, this will temporarily impede his arm, but more importantly, it will allow EASY access to slide your first grip in deep. roger's method of using his hip sounds cool though. i'll try that next week.
if your partner's wrists feel weak right when they grab it, then tell them to straighten their wrist before they grab. the problem is that although deeper is normally better, sometimes people reach so deep that their wrist bends into a weak position. thus they achieve a deeper choke, but their wrist is so bent that trying to apply pressure through the wrist feels like you're wristlocking yourself. pull back the grip just enough to make the wrist firm again, and then take the grip. if for some reason you try to choke at that point and it's still not deep enough, "shake the baby."