340 Gets Terrible Gas Mileage

As to Champion plugs;
My 11/1 alloy headed 360 has run the very same copper Champions for over 100,000 miles. They will still idle at 550rpm, pulling the ol' Barracuda around the parking lot at under 4 mph. And she will hit 7000 right after that. They were new in 1999.
I planned a track day in 2004, so pulled the plugs for a look, and screwed them right back in. She later that day, ran 93 in the Eighth with those already ancient plugs.
As to the TQ carb;
For fuel mileage, that spreadbore/metering rod design is really hard to beat. I used to install them on anything/everything.
Having said that, there's nothing so wrong about a 650 Holley that I would waste money to replace it; you will very likely Never save the purchase price, in fuel economy, for several years.

IMO, I'll bet 100points that your cylinder pressure is very low, and your cruise timing is just not there.

When the cruise timing is retarded, peak cylinder pressure is never achieved.
But it's worse; the A/F mixture may not finish burning in the chamber but rather continues burning/chasing after the falling piston. The still expanding gasses exit the cylinder at or near 100* ATDC, before transferring all their energy to the crank, and instead put it to use heating the ports and exhaust system.
At the other end, with headers, and a "big cam", overlap may be so large that at low rpm, a sizeable slug of just-inducted mixture may zip right across the top of the piston, and exit into the exhaust system, before the exhaust valve closes. That is literally sucking, your fuel mileage right out the tailpipe.
A street engine with a big cam, for fuel economy, has to be geared to cruise well over 2000, perhaps up to 2400 rpm to shut the door to this phenomenon ...... which itself is counter-productive to fuel economy.

Big cams in low-compression engines, kill cylinder pressure. This makes the engine lazy and sluggish at low rpm; so you are forever deep into the throttle to get some reasonable acceleration, and during cruise, the throttle will be open further than would be the case in a high-compression engine, both of these traits kill fuel economy.