Unfortunately this is an old post, but I'm having somewhat similar issues with new-to-me 2007 Vulcan 500. Mine actually will NOT run with the choke on and it takes 4-5 starts when cold to get it to stay running. I got it 2 weeks ago, dumped the 6 year old gas out of the tank, of course that didn't fix it, so I pulled the carbs and cleaned them by hand with B12. Bike was able to start and run after, but as stated above it doesn't like it when it hasn't been warmed up. I put 150 miles on it last weekend, but it isn't 100%, so I did some reading and saw that the pilot SCREW is supposed to be 2 1/8 turns out, so I pulled the carbs again and unscrewed the pilot JET 2 1/8 turns, now the bike won't even start. So now I've pulled the carbs for the 3rd time last night and put them in an ultrasonic cleaner that I bought from HF last night on the way home. Here's my big hang up, I don't see a pilot screw. I've attached a pic of one of the carbs and a pic of the parts diagram. Where the heck is 16014??? The pilot jet I unscrewed is 92064, which I'm assuming is supposed to be screwed all the way in, like it was when I pulled the carbs the first time. I feel like this is gonna be, super simple making me feel dumb, but I don't care at this point. I'm already tired of pulling the carbs.
And to the previous poster from 2 months ago, that is most likely a bad float valve. Expensive little suckers, but that is the #1 culprit on our dirtbikes.