Carburetor issues, running rough and high idle

It likely isn't destroyed, the trick will be finding a shop that knows carbs. Those can be hard to find these days. I would suggest finding a cab company or two that have been around a long while and see who they took their cars to back then. They should have the tools and knowledge to adjust it top match the vehicle. There are some "antique" tools needed to adjust the E4M properly.
What was the issue with the original carburetor?

Which engine do you have the 5.7-350 or the 5.0-305? The 350 has never been great at mileage but 11 is low for one in a car. The 305 usually does a little better but in a large vehicle they are still not real good. Most of the time the replacement carbs are set up with the specifications for a generic 350. You bolt them on and then fine tune them to match the engines wear and any odd items. Did it have a general tune up prior to the replacement carburetor? IE plugs, wires, cap, rotor? How is it mainly driven, long drives or short stop and go like a taxi?

The short drives are not helping but even then you should be seeing better mileage than 11. 20-23 out of a 350 is very good. Did it suddenly drop or did it slowly degrade? Did the tune up help at all? I'm guessing not very much? A drop like that could be from a timing error if the chain jumped but I would think that was checked first. Did the carburetor change do anything? Was it idling high with the original carburetor?

Not having tools to work on a carburetor isn't surprising really. Timing would be the timing chain in this case. GM used a silent drive chain on that vintage. The lower sprocket is iron while the top is a plastic material. The teeth fail and they can jump a tooth or more. A quick way to test that would be to check the spark timing with a timing light. You should have a sticker on the radiator support showing the timing in degrees btdc. If that is way off then it's possible the timing chain is part of the problem.