Ethan, how much lateral flexion do you usually do? I saw you do it once on each side in the video, but I'm not sure if you usually do it more. I do each side at least 5 times before I ride, then work on flexing his body at a walk or eventually trot and lope if he can handle it at those speeds.
In addition, I teach my horses to drop their head two ways depending on the amount of control necessary. The way I prefer is called "winging out", where I extend my arms out to the sides with little to light contact on the bit until they drop their head then immediately release. It's also easier to relieve the pressure the exact moment he gives with this method.
If you need more speed control, however, inside rein slightly up and outside rein toward the hip works as well. The upside is that you have the option of more contact if you feel you need it but you need to have really good feel to do it correctly so the horse doesn't get confused or frustrated when there's no immediate release for doing the right thing.
When I got Sock, he had no clue what I was asking at first when I winged out on him. What worked for us was a loosely adjusted German martingale for a day. It was just tight enough to put a little downward pressure on the bit to give him the idea. Some horses might take longer to get it, but if Frank is as smart as Sock (and he seems to be) he should get it fairly quickly as well. I would suggest waiting until he's softer in the mouth, though.
I agree with Mood. You can get the same sort of give from larger circles than the ones you're doing here.
How quickly to you give him release when he gives to you? Is it immediate or do you hesitate for a second or two? Also I'd be interested to see what he does if you just gave him his head. Some horses will take blatant advantage of it, but others will thank you immensely!
Sorry for being long-winded, just trying to explain the best I can. :) Keep reading H&R. Lots of good stuff in those!