I was in a unique position to have trained with Royce Gracie for a while several summers ago.
One time after he was finished twisting me into whatever particular shape that he wanted to see that day, we left the mat and walked over to the free weight area. Royce laid down on a Bench and began to Bench Press. I could tell that he had either never performed this exercise, or at least was not very good at it.
There was 135lbs. on the bar he took it off the rack and performed five reps with it. He barely got the fifth rep! I knew then that while it’s always better to have more strength than your opponent, all other things being equal, strength is not the most important thing.
He then went over to the Treadmill warmed up a bit and cranked it up to 9mph. He ran at that pace until he reached one mile. When he got off his breathing was hard, but not what you would expect for someone who just ran a pretty fast mile.
He then got on one of those stretching machines (the type where you sit on the ground and crank your legs apart). I watched him crank it so that his legs were all the way out, one on each side. Then he kept going to the point where his legs were several inches past that point. It looked sort of freaky.
The entire point of the story is to show you that you don’t have to be the strongest guy on the mat in order to be the best. Of course, you better have other tricks in your bag. As you know being a Jiu-Jitsu practioner, technique is what will further your game more than anything.
Since the mid 90’s when Royce ruled the mats, much stronger guys have taken his place. However, that does not negate the fact that technique is still king. These strong guys are also quite proficient at technique. Strength is simply a very important helper. As a former High School and collegiate wrestler I used to literally toy with guys in gym class who were as much as 50lbs. heavier than I was…technique ruled!
As far as exercises in my opinion I think you need to work with more explosive movements: Clean & Press would be a real good one to incorporate. Naturally, keep the Deadlift, drop the Bench Press (I won’t get into why here). Add lot’s of Dumbbell work as it gives you the chance to work each arm independently, sort of like a grappling match.
I would also do sand bag and log or rock lifting work if you have the opportunity.