Fighting for grips/chokes on back mount

Does anyone have any tips or tricks for securing the choke from back mount? I find that I am not very effective at fighting for grips when my intended victim is defending their neck. I tend to waste a good deal of energy fighting them for the cross-neck grip that most rear chokes begin with. By the time I end up securing the grip, my forearms are burned out and my choke is ineffective. It frustrated me last night when I was unable to submit a brand-new student for a full 5 minutes, as he kept fighting each grip and ripping my hands away.

My instructor chuckled and said, "keep trying." Looking for tips on sinking in that choke.