Welcome to the club. There is nothing like being on the mat. It is one of the few times in life where my mind is actually still.
The hardest thing to ever get used to is relaxing on the mat. I was told it so many times and now I find myself telling others a lot. It is one of those relax and enjoy the ride kind of deals.
The static strength thing is something very interesting to me. I train a lot of dynamic strength stuff and the only real static strength stuff I do is planks. I don't know if there is an exercise that you can do that simulates holding someone in the guard position. That might be one of those sport specific strengths that develop as you develop.
Feel free to ask anytime you have a question. I log all my BJJ training in my training log in addition to my strength workouts.
What we think, or what we know, or what we believe, is in the end, of little consequence. The only thing of consequence is what we do. -John Ruskin