John,
I like your approach to this. It has to be something. I'm up to my elbows right now but did a quick look at the SM. Para E-77. Inspection and Repair, covers the rocker arm. I've never had a problem with mine so I've never disassembled it.
But. Here's a digital copy (good for travel! lol)
http://48cj2a.com/images/manuals/UniversalServiceManualForJeepVehicles.pdf(big download, 56MB and 281 pgs)
To paraphrase the inspection part, it seems to concentrate on cleaning the shaft and oil holes. Ensure they're open and the shaft isn't worn or bent. It then moves to the adjusting screw holes and if needed chase the threads. Replace the screw or lock nut if either are damaged or deformed. Same for the hole in the top of the rocker arms.
I actually like the idea of swapping your #1 with one of the others, i.e. #2 rod. To me this would be an easy shade tree check to see if your problem is with the replacment rods or, in fact there's something wrong at #1. Could be both.
If you find the problem is with the rocker arm assembly, I'd suggest contacting Harry Sheets for original parts (including rods):
http://www.midwestwillys.com/