So after rolling with me himself, my coach offered me this: Don't attempt a submission until you've managed to hold your position for a full minute. If you can do this, you'll get a lot better.
That should be quite a challenge, but I'm determined to try. People will likely think I'm weird for getting a position and just hanging out (if I am even successful at it), but I'm sure he's right about how this will help my game, so I'll do it.
Should be interesting.