Backing up a bit, no new info, but after you mentioned systematic
I would slow this effort down and rule some things out
1 - Pull all plugs and read them
2 - Check all wires for resistance per foot using an Ohmmeter (should be all the same per foot, although different numbers) paying close attention to any wires that fed plugs that were different than the others
3 - Compression test (optional as plugs are out, but would be good to find a tight valve, etc)
4 - Check TDC on your balancer
5 - Check that the engine has a good ground and the distributor has a good ground
6 - Check initial timing vac advance disconnected (anything over 14 will run well if the balancer is right)
7 - Adjust idle a/f when hot and choke open for best vacuum
If you find something on any one step, note it, fix it, or look for a cause, then continue with the list. If it still doesn't run well, we'll give you another list. The key though is to continue with the list even if you find something, don't just yell "eureka" and see how it runs, we want to rule it all out and then allow a basic tune once you find the issue.
It seems like between the rain, the trip to the shop, and all the posts that this is turning into experimentation and as you said, we need to be systematic.
If after all that, if it still runs poorly, then we need to think about going inside, but if you execute this list in a calm, zen like manner, slow and methodically, you'll have some answers, or a well-running engine