Forget karate, it's just a series of conditioned reflexes that will allow any experienced technical fighter to make you "zig when you shoulda zagged." Just practice the punches and kicks at various ranges a few times a week, striking solid objects to build up your striking speed and power. I say go to the BJJ school, but THINK about the moves to learn how they work. Also study the moves, going through them SLOWLY before just trying them in sessions; that way you can go over them in your head, even unconsciously while you're asleep, and you'll find yourself suddenly understanding them and how to apply them. Finally, try to figure out what the OTHER person is trying to do first, before you react; the way to beat a wrestler, or anyone, is to try and figure out their strategy (i.e. what they're trying to do) and come up with the best counter-strategy; this involves both beathing their moves, as well as just wearing them out (let them think they're putting a hold or punch-etc on you while you're just blocking it and they just get tired).
Well, like I said, I would kill to learn grappling, but there's just no time right now. There's a pretty good BJJ school like two miles away, too, which absolutely kills me. It's not like I'm doing something 24/7, but I work on average 3-4 days a week plus school, and I've already requested Tuesdays and Thursdays off for karate. Unless it was one of those places that's always open, I'd probably never be able to attend classes. Which sucks. Immeasurably.