You say you have the 360 V8. The 318 V8 of those years had a unique carb problem.
It occurred (slowly) when the air cleaner wing nut was tightened too tight. It would warp the upper half of the carburetor, to the point where it no longer sealed properly to the bottom (bowl) half of the carb. When that happened, the engine would run rough, primarily at lower rpms.
The fix, per the Chrysler warranty procedure, was to get a sheet of sandpaper and lay it on a very flat surface, like a thick piece of glass. Then take the carb’s upper half and rub it in a swirling motion on the sandpaper. It didn’t take long for the wear pattern to show the mating surface was flat once again.
This primarily happened on the carb that came with the 318 engine (Carter?) from the ~76-~78 timeframe. I did hundreds of these. I don’t recall it on the 360 carb, but you may want to check.
Car came in to us on cool day; started up sluggishly and then idled just fine after. Since changing old battery terminal turns 360 over immediately but begins to sound real rough-running in the heat. Now sounding like raggedy all of the time in humidity.
The mixture may be too rich. Check the choke operation first. The choke plate should be fully open when the engine is warm. And check the idle mixture screws for proper set-up. When the engine is idling and fully warmed up, if you turn a mixture screw clockwise (to allow less fuel), the rpm should noticeably decrease by 1/2-3/4 turn.