Free-flowing headers can be less efficient than cast manifolds
if both are the same diameters and flow. This is because of how much heat that dissipates into the engine compartment.
Generally with tech up to the 90s, you can estimate 1/3 of the heat produced by combustion goes to turning the crank, 1/3 to pushing the exhaust out the tailpipes, and 1/3 as waste heat. When you improve the flow of the exhaust, it would make sense that the other two factors improve, right? Not quite.
If the power production hasn't changed, then the amount applied to the crank can only stay the same. This is because the power follows the path of least resistance, and your headers just became the weakest link instead of the restrictive exhaust. If it's not pushing the exhaust, then it simply becomes more waste heat. Again, this is comparing hypothetical cast iron vs tubular steel. The cast iron will slow the heat dissipation rate. As long as they don't melt

you will have two of the three routes improved and the power going to the crank will be the easiest path for the power to apply itself.
For mileage your actual goal should be
efficiency, meaning converting a higher percentage of the fuel you take in, to useable power. The more efficient your burn is, the closer you will get to the 17:1 ideal stochiometric ratio. 1980s tech needed about 14:1 or even 13:1 because of inefficient designs for heads, cams, etc.
Swapping Vortec heads on would allow you to run leaner, because of their combustion chamber design. Swapping aluminum heads on can also help, but only if you increase the combustion ratio to take advantage of them. It will be the improved combustion that makes more efficient burning, not the material of the head.
Keep the velocity of all your airflow as high as you reasonably can. This will help on the intake side by keeping the fuel droplets in suspension instead of falling to form puddles on the port floor or even inside the chamber. For the same CFM a completely unrestricted exhaust has relatively no velocity, producing more waste heat. For a typical street 350, running well, I like using 2-1/4" dual pipes all the way back behind the tires. Cats and mufflers don't have to be restrictive. Some of the ones with valves in them look interesting but I'd pin my hopes on Cherry Bomb Vortex mufflers and any cat you can see through with a 2-1/4"ish diameter. The rare metals still do their converting, as long as the exhaust passing through them has heat.
Sanderson, Speedway, and a few other places have cast iron headers. A lot of people put faith in their Corvette ram's horns, but most of them are about 2" outlets just like 4x4 stock manifolds. The ones that are 2-1/2 are in the "if you have to ask..." price range. Wraps and coatings can slow heat dissipation too, as long as you're willing to accept the trade-offs.
There's no replacement for displacement. That goes for the size of the engine, or the size of the blower. Yup, blower. The Weiand 142 is one of my long-gone friend's favorites. I like the way belt-driven blow-through chargers can usually be installed without so many custom parts. These include the Procharger, Paxton, Vortech, etc. Since they will change the pressure of, well, everything between it and the tailpipe then all three factors will increase. This is more efficient than an unblown engine, but you will have to re-gear to a taller ratio to see an improvement in MPG from this. Find a spot where your charged engine makes the torque it needs to do the job you want, see what RPM the old combo made the same power at, and use those numbers to determine how much (in percent) you can change your ratio.
The same goes for turbochargers, but typically they don't do their work at low engine speeds. You'd have to go backwards (shorter/lower gears) to deal with the range they do their work in.
The large block engines are another way to get your mileage. My mentor had a 396w/.030 over, that got over 20 MPG in a station wagon using what was called a Mil-O-Mor cam that Isky had (no longer in production). 500 inch Cadillac engines make their power WAY down low, as in a power peak stock near 2000 RPM. If you gear your rearend to work in that range, you can still create a LOT more power than an 80s 350 can. We had a 472 in a Studebaker 1/2 ton that got 17ish and the only time it ever saw the highway was on the way to Bakersfield once.
In general a stick-shift is more efficient than an automatic at transferring power from the crank rearwards. A lower rated unit like a 350 or 4L60 will be more efficient than a 400 or 4L85, largely because of how much power goes to becoming torque converter heat.
Roller cams have the capability to be more efficient than flat tappets but only if they are ground with higher ramps and shorter duration (and with those two comes less overlap). The stock rollers from 1987 through the LT engines and up to the last Vortec in 2002, were very conservative. Aftermarket RV/tow cams will be more efficient. They are available for Caddy and BBCs.
Overdrive can be great, but having an extra gear down low and using direct drive in combination with a taller gear is more efficient. At 1:1 the internal configuration is passing the most power it can, all other gears and idlers soak up energy. This is the advantage that TCI 6x transmissions offer, even though they are automatic. The driveshaft will also rotate fewer times for the same mph, so harmonics don't get as bad and momentum is lower. Aluminum driveshafts have a greater part here than in wheels.
12-bolt rearends are more efficient than 9-inchers. This is due to the location of the pinion gears and the resulting pitch of the angled gear teeth.
Rotating mass should be lightened. Honda engineers (yes, no one wanted to give them credit for years afterward) determined in an annual MPG race with other manufacturers that a light flywheel with little mass is more efficient that the heavy flywheels with more stored momentum. Driving techniques also included
accelerating up hills and
coasting down them. Why use throttle to get to the top of a hill after coasting, and again to increase momentum down a hill? You can cut your time on the throttle in half by coasting down a hill and accelerating up. As always, roll into and out of the throttle instead of stomping on it. This is where the "imagine an egg between your foot and the gas pedal" comes in.
Fuel injection, even electronic, is not the big aid that one would think it should be. It reduces warm-up time and smog emissions. Introducing the fuel closer to the combustion chamber improves the chances of the droplets staying in suspension. Flatheads could get better than 20 mpg with a carburetor though. I could hit over 35 mpg in my first car, a slant-6 Duster. Carbureted Hondas hit higher ratings than the bulk of today's hybrids. A custom tune can help an electronic fuel injection system follow a curve closer to the ones the carbs produced, with some other advantages (like changing the tune depending on if your loaded or not--the purpose of VVT and other technologies). If you decide the expense won't be recovered in a reasonable time then stick with spreadbore carbs like Quadrajets and Thermoquads. The Holley spreadbores "just aren't right" but that has more to do with quality control and tolerances than any conceptual problem. The spreadbores can act like 2-barrels sipping fuel when you don't need power and opening up to 750-900 cfm if you need it. Squarebore carbs are meant for situations that don't often involve cruising--like making good numbers for advertising (or racing

)
Correct or at least appropriate steering and suspension settings with components in good condition (right down to the bearings and races) will reduce rolling resistance. Wheels with flat hubcaps or a flat outer surface that's flush with the body lines (like high-offset wheels) will give less air resistance. Pulling in the window frames on pickups and sedans helps get the odd shapes out of the wind and also seals the alternative paths for the airflow. Mirrors, raingutters, side trim, bumperettes, door handles, wipers and side windows rolled down all impact airflow. Open wind wings to a certain angle (different for each vehicle) or shut all the windows--even if you have to turn the AC on!
The best speed for mileage varies with each vehicle, but it is
not 55. It is the point where the sum of all mechanical resistances, becomes less than the effect of air resistance. I've found on most of my vehicles that it seems to be 62 MPH, but improvements have been made in both factors over the last couple decades.
If you are mind-boggled by all the tips and factors involved, then you are close to ready to tackle the mileage issue. The last brain-frying tip I will throw at you is--"You have to think of ALL those things at the same time!" Every element in your package or recipe has to complement every other element in it. Plan your choices ahead of time, and stick to the plan instead of throwing one or two items at something that had poor mileage to begin with.
I don't expect to go better than 17 on my truck, because I won't get the returns on my investment for adding more to my package. Let's see who can get there before I do (out of the people who don't already get it ahead of time).
ps (I've noticed I get about 10% better mileage if I pay about 10% more for the 100% gas available around here, instead of 10% alky--MY TRUCK IS SOBER!--but the mileage issue is essentially a wash as a factor. I didn't have ANY grainy crap in my float bowl when I opened it up after 6 months today.)