Starts hard when warm and hesitates to accelerate

I have an '89 300TE (150K miles)with two symptoms that I suspect are related. I have recently changed the plugs from Platinum to Bosch Copper - OEM pt# with fresh and desireable performance as a result. However, when the engine (3L I6cyl) is started hot - it will stall immediately. If the accelerator is held to 1/3 or so - it will run rough for approx 3-4 seconds and then settle at a good idle. This occurs on every hard start. The second condition is that when the car is accelerated - on occasion (not often) the car hesitates - it idles well and doesn't miss - it just sits at an idle momentarily and then jumps into accelerating. Do I have governor problems?? Could the cap/rotor be responsible??

The car is in Michigan - when cold the start is good. The car also starts without fail after many days of not running. While driving, the engine performs well. No fault codes or CEL is present.

While I'm asking - any advice or opinion of rear differential life expectancy? The car has 150K miles - it's ok now but I've had diff problems on other models (123 particularly with high miles).