Jack,
I had a problem kind like this with one of my Kenworths awhile back. Like I had stated I would have "issues" with cranking on wet or humid days. If I slaved or jumped the truck it would start and be fine afterwords.... But I was 24 volts at the batteries.
Finially came a day where she had nothing, low power to accessories but no crank.
I started at the batteries. All showing 13.2 volts checked all the battery cables and replaced all the had corrosion in the wire itself under the coating. Nothing.... I then started tracing the main harness from the battery box unbolting the harness and pulling it from the casing. (a 264" wheelbase semi tractor) Finially I found the spot, in a place where the case and the protective coating had split under the 66" sleeper and all the roadsalt from winter roads had found its way into the wire... A 5/8 inch power wire was totally green from corrosion and under the green all the wires were broken except 1 strand in the middle, still connected. So all the corrsion was a huge resistor and finially when there way only 1 strand intact there was not enough surface area on that strand to push enough voltage thru to crank that 575HP caterpillar diesel.
This is more than likely your problem, start tracing your main harness..... This will suck but once you find it you can butt connect repair the bad area. Make sure you soldier all the connections and shrink wrap the repaired area and the brush on more paint on wire coating over the shrink wrapped area to keep mother nature out.
Good Luck.