You turned on the headlights and it died? What battery test did you do and what voltage do you have? Did you get codes for the TPS or MAP sensors. Why did you spend the time and money to replace them? Unplug the injector and plug the noid light plug into the fuel injector connector. It will flash when the injector would be is commanded to fire. What you test light flashing when you cranked the engine?

Just because the truck is emissions exempt isn’t really a good reason to remove the air injection and EGR systems as long as they are operating as designed.

You said the water pump is belt driven so I still don’t understand what you meant by the “swapping in a better pump to stop killing batteries” comment. How would a mechanical water pump be killing the battery?

Removing the engine to replace the core support makes as much sense to me as removing the door to replace the core support. As we have been telling you, there is no way to know what size bearings and pistons to order without measuring them first. Are the cylinders bores going to need to be machined? What about the crankshaft? You don’t need a kit to replace the valve cover gaskets. The only other gasket you would need is the upper plenum gasket. On the other hand, you could buy a cylinder head gasket kit which would include all the intake manifold and valve cover gaskets.