It's been a while since I've last posted about this, but I thought I'd update this in case anyone is having a similar problem. My solution: I replaced the petcock with the 2003 yamaha raptor 660 petcock a lot of people have mentioned here:
http://www.ronayers.com/ProductDetails/N/687/SKU/808680For about $25 (including shipping), all of my problems went away. My bike runs great, no longer dies intermittently, and doesn't leak fuel from the carburetor vent hoses any more. This is after trying a bunch of other stuff:
-running Sea Foam through the carburetor a couple times
-completely taking the carburetor apart, cleaning it, and checking/adjusting the float, twice
-taking the old petcock apart, verifying the diaphragm was intact and the fuel screen wasn't clogged
-replacing the fuel and vacuum lines, just to make sure they weren't leaking
-tinkering with the idle to make sure it just wasn't too low
There may be a few things I did I'm forgetting. At any rate, this problem was driving me nuts and it all went away with one simple part replacement. Thanks for everyone's help!