Thanks for all the suggestions everyone. I ended up getting a master cylinder rebuild kit from a local shop that fixed the issue.
I finally got the bike to start consistently. My timing was too far advanced and the rear cylinder was being starved fuel on start-up, making things a lot more difficult. I adjusted the spray pattern of the main jet which helped a bit, but I'm thinking I still need to bump both the slow and main jets.
After sorting out a few other small issues, I decided to take it for its first ride. For some reason I couldn't get the clutch to adjust properly. No matter what I did, the clutch would ride every time I would give it any throttle.
Upon popping the primary cover, I found this;
Pretty much every one of the pressure plates were destroyed like that. Nice huh?
Note to self;
Next time you buy a bike that's beat to shit by the previous owner, check the clutch before trying to ride it. There's a good chance the last guy blew it to bits before selling it.