340 Gets Terrible Gas Mileage

Yes not sure what that valve does so you are right this would be something to look at.
That valve is a delay valve for the vacuum advance on the distributor. I would bypass it and run the vacuum line straight to the vacuum advance from the carburetor. It is an emissions device designed to lower tailpipe emissions and is not conducive to performance.

But that valve is not your problem. Check the initial timing and report back with where it is.