My 340 getting 6 mpg

In my experience, once the A/F ratio is set correctly at ~13:1 full throttle and near 14.5:1 cruise, timing is the most important tuning issue for FE. 340's like about 34° mechanical advance and as much vacuum advance as the fuel will allow which is typically about 51°. These are crank degrees, not distributor degrees. A timing tape or marked damper are a must to set up total timing correctly.
My preferred setup is to use an 11° (distributor degree) advance plate (FBO works) and set initial timing at 12° (engine) advance for a total of 34°. (2*11+12). Then use a vacuum advance unit that is market for about 15° (Dist) advance. The vacuum point at which vacuum advance starts is adjusted by the Allen head screw in the vacuum canister accessed through the nipple.

Granted, I was using a mild cam during the '70's fuel economy crisis, but with tuning and an electric cooling fan and desert cooler radiator, I got my 340 to get 22-24 on the highway (2.94 rear gears). Here in Denver area, my current 340 with a 284/484 cam and 10.25:1 CR gets 16-17 MPG using the tune above. And it produced 300 rear wheel HP on the Mile High chassis dyno.
Let us know the distributor configuration when you get things checked out.