I had a guys GMC squarebody in my pole barn about a month ago. K15 350 quadrajet. It would not idle at all. Smoked so bad it looked like a wet leaf fire. Backfired thru the carb, hitting on about 5-6 cylinders. He said he was tooling down the road and it just started acting up. He had oil foulers in two cylinders. He wanted to jerk the motor and replace it. I'll admit that I also thought the engine was bad.
He didn't tell me at first that he noticed it was loading up a little at idle so he decided to rebuild the carb. He had never rebuilt one and totally fubared the job. It was dumping so much fuel the dipstick showed two quarts over full and the cylinders were washing out.
I checked compression, electrical and fuel and within about 45 minutes confirmed the carb was no good.
I put another quadrajet on it, changed the oil and the spark plugs and it is now running like it did in 1978. No smoking, no misfire, nothing.
The best troubleshooting follows a method, or a tree or a process, whatever you want to call it, but as a former ASE tech, random guesswork leads to frustrations and throwing wrenches, parts and money out the garage door.