tmarti96,
Engine speed sensor(crank speed sensor) would seem to be the culprit.
But could be something else.
The fluctuating of tach, alternator quiting, tc messin up some what points to it.
But a/c and no trouble with the trans shifting doesn't.
The engine speed sensor (mainly its connector,loose,burnt, dirty pins are usually the problem not the sensor) indirectly help run a few things on the truck.
Tach, vehicle speed control(cruise), asd relay(generator field), torque convertor electrical engagement, along with vehilcel speed sensor(VSS) and throttle position sensor(TPS) determines when to shift auto trans in and out of overdrive and their mite be a few others.
Check your connection for engine speed sensor.
Check grounds. I'm not sure but several of the items you are having trouble with mite have same ground location.
Check gound to PCM if I recall correctly the ground(for sensors) is located by injector pump on head or intake manifold in front of intake heater.
While you looking at grounds check all corresponding wires(loose broken,shorted) /connections(loose, loose,dirty,broken,burnt pins).
You mite be able to get a fault code out of your PCM.