What position is your petcock in? ON or PRI? Make sure it is in the ON position. Also check around the carbs for any visible fluid leaks. Inspect the fluid coming out of the suspected hose and verify what it is.
I'm at work now, but will check the petcock when I get home tonight. I'll doublecheck but am 99% sure it's gas that does leak out of the hose. It looks like there's two hoses right next to each other that both sort of just hang down and appear to not have a stop at the end. The one that leaks is more towards the left side of the bike than the other (although they are side by side pretty much), if that makes sense. Sorry - no smartphone to be able to upload pics!
Assuming I have fixed the stalling/dying issue with the new, better gas and additive plus an increase in idle, do you guys think it would be safe to drive? If this does end up being a carb issue, I just don't really trust myself to correct it myself - even with everyones infinite wisdom and expertise on here!! - so would probably rather just take it in to have it looked at. But I'd have to drive it since I have no truck/trailer to haul and just want to be sure I wouldn't do more damage or something. I'll check again when home, but like I said, I don't THINK it just leaks continuously, only a bit when actually pouring fuel in the tank.