Fuel Starvation, no apparent cause!

Could you have a blockage on the fuel hose to the carb?

What if you did the following when you have the problem: disconnect the fuel supply hose and try blowing into it. If the floats are down (low fuel level) and the needle valve is stuck shut then you will not be able to blow into the bowl. If this is the case then you could carefully remove the bowl, check that the needle valve can be moved and try blowing into the fuel supply hose again, if you can then the valve is sticking, if you can't then you have a blockage.

What did the spark plugs look like?  Were they light grey as if they had been running lean?  One of my carbs was doing that same thing and the engine would cut out only at wide open throttle. Plugs on that one side were grey.  I discovered that the float arms in that carb were not set quite parallel to the carb flange per the manual and more interestingly the two float arms had been squeezed in towards each other slightly but it was enough to rub on the carb body and cause fuel starvation at high rpm.  This bend inward was very slight and was easy to miss so look close and see if the arms move freely up and down without contacting anything near by with the bowl off.  When the arms on my carb were set to the right parallel dimension and unbent inwardly the float valve was free to do its job and the problem went away.  

Maybe it is vapor lock, do you have a return line?

The fuel lines from the tank to both carbs have been replaced entirely with no effect

Yes a return line is installed. Larry Olson, was your fuel starvation intermittent or constant? My float arms do seem to move up and down freely with the bowl off and the carb has been stripped and inspected by a proffesional but they could have missed something. Did you use the proper gauge to set your float arms or just tweek them by hand to how you thought they should be?