What's the best way to find a dead cylinder?

Good question. The answer is no, not yet. Here's what I'm thinking. The motor in my Duster was a replacement engine installed 36 years ago, and now has over 105K miles on it. I'm not sure how much life this engine has left in it. I suspect that it had poor maintenance prior to my ownership. If I can solve the problem I currently have, there's no guarantee that another problem won't pop up shortly thereafter. I plan on keeping this car forever and driving it a lot. There's one school of thought that says to cut your losses and just go with a new engine. That way you can enjoy many years of trouble free driving. Since the current engine now in my car isn't the numbers matching original, it's not that valuable. If it WAS the numbers matching motor, no question - I'd keep it and rebuild it. But this isn't the case unfortunately. Yes, I'm planning on running the test you mentioned, and I really appreciate the technical advice. I just don't want to "throw good money after bad" as the old saying goes. I definitely haven't made the decision to buy a new motor. I'm just in the "thinking about it" phase right now. There's a place called S and J Motors that will sell a rebuilt long engine, balanced and with mild head porting work for about 3K. What's your take on all this, Rusty?
I think you're on the right track. Regarding the "crate engine" approach. If you plan to start with nothing, in other words, you want a "TOTALLY" complete new engine, just be advised it will not be cheap. Someone will have to come up with an entire long block. That's the easy part. Then, they have to locate all of the tin, the valve cover, timing cover and oil pan. Next is all of the various fasteners. That takes a lot of time and effort. It's not something that's going to happen for say 2500-3500 dollars. Sure, a basic long block can be had for that, but people seem to forget about all the other details. That is of course you plan on using all of that from your present engine. If you want a "plug and play" approach, just be prepared to pay someone for their time, parts and effort.