The two things that occur to me are bad needle and seat, causing it to load up with fuel, or a bad fuel pump causing it to suck fuel through the impulse line while it's running. I'd start by opening the crankcase drain plugs (look on the bottom front of the block, underneath the Y-pipe). You'll probably get a little oil out of them, but if you see more than a small dribble of gas, it's probably the fuel pump.
To check the needle and seat, per the FSM, you have to take the carb off and invert it, then apply 5 PSI to the fuel inlet. It should hold that for at least a minute. To be honest, I've never checked them that way. I've replaced a couple sets mostly for peace of mind, but you'd either need to rig up something with a compressor line or buy a hand pump. Dealer's choice on that, the needle and seat are about $15 each.
