Sure its not poor connections making it seem like weak batteries? Maybe starter on its way out? The amount of amperage draw on the batteries required to kill them in 5 seconds or less will definitely be melting the cables and other wiring.
Most of the positive and negative battery to vehicle connections are done at the starter on those. Make sure the group of positive and group of negative cables are tight on their studs on the starter. There is also a harness in the battery box, with 3 small fuse holders in them. Those fuse holder love to melt. Remove each fuse and check for a burnt terminal. That harness has 2 connectors near the starter. The terminals on those like to turn black and burn. Sounds like a poor connection, as others have stated in order to kill a battery that fast, there would be melting involved. Have you checked battery voltage with a meter? Or assuming they are dead because of no action?
