If baking soda laden water got inside the cell of the batteries it could ruin them by neutralizing the acid but I don't think that really fits with your symptoms of starting then dying.
The back pressure code can trip from things like disconnecting the electrical plug to it. I can't think of anything related to it that would stop an engine that is already running. This code usually goes away when you clear with a reader or unhook the batteries for a while. (or take the whole backpressure valve out
)
Those crank position codes are not any that I have heard about false positives on and youv'e got 3 or 4 of em. Seems like a logical first place to start. CPS's are pretty notorious in these trucks.
