I found the cause for my fuel flooded airbox. It was the carburetor bowl vent tube. It looks like mud daubers tried to build a nest in the end of the rubber tube where it hangs near the ground, clogging it. I popped the tube off of the vent nipple between the carbs and tried the fuel level check again, and it's just a whisker above the edge of the bowls on both sides.
So now all I have to do is check the cylinders for gas buildup, change the oil, replace the air filter, unplug and reconnect the vent tube, and I should be back on the road.
Thanks for your help, folks - I don't know what I'd have done without the forums here.
Dave