I'd start looking at connections downstream from the batteries, like wherever the power to the vehicle branches off the starter circuit, for example, and also at the grounds. Your symptoms sound like a connection that fails under load somewhere.
I don't know what you mean when you say dielectric grease is expensive, but for about $18 you can get a tube of Dow DC-4 that'll last pretty much a lifetime if you're not in the industry.
The Constitution needs to be re-read, not re-written!
If you can't handle Dr. Seuss, how will you handle real life?
Current oil burners: MB GLK250 BlueTEC, John Deere X758
New ride: MB GLS450 - most stately
Gone but not forgotten: '87 F350 7.3, '93 C2500 6.5, '95 K2500 6.5, '06 K2500HD 6.6, '90 MB 350SDL, Kubota 7510