360 running on 4 cylinders

If you have a significant leak down problem, you'll be burning oil. If it has the compression you said it does, that's enough to run smooth. I like to keep a spare module in the trunk along with a ballast resistor, just in case one craps out at an inopportune time. I'd get a spare to try and keep. I have an extra distributor in the garage for the same reason. It's rare a reluctor or pickup coil will go bad, but, not unheard of. I'd still try dribbling a bit of fuel into the carb to see if the idle smooths out or not. First one side, then the other. You may be getting some weird vacuum leak once it warms up. I know some of the stock intakes (like the '73-8 440's) would crack through the bottom, and sometimes into the EGR port. They would sometimes run fine cold, but, once fully warm, that crack would open more and they would lean out, idle rough, and run hot. Maybe you have something like that going on.