Congrats on the new Dodge project. Looks very complete and good shape-- a good start there.
You mention about doing a carb rebuild----------hhmmm-- two years ago I went to Montana and picked up a Chevy G506 1 1/2 ton truck. It had been sitting for about 10 years. I get it home and finally a year later I get time to tinker on it. Hooked up a clean 5 gallon can so as to eliminate the fuel tank crud possibilities. It would start but not stay running. Peed gas out the tube at the top of the carb.
Gave up and headed for town for a rebuild kit. Parts Guy tells me an old trick. Before putting out the money and time to rebuild the carb try using a small hammer to whack on the side of the carb. Use the wooden handle -NOT the steel head of the hammer so you don't break something. With fresh gas, it may unstick itself with a little gentle persuasion.
It stopped peeing fuel out the top tube and continued to run, idled great, runs good. Starts right up. No hesitation on acceleration.
It may be worth a try ----your mileage may vary.