When you disconnect your system from power in the fall do you have the power turned on at least 24 hours before you turn the A/C on? Just asking as I think that Armstrong uses the capaciter in the off cycle as a crankcase heater of sorts and if power was not on for 24 hours then the unit could have had trouble starting up and locked itself. Just a thought.
I also agree that if the compressor is changed the manufacturer may check it and determine that it is OK and charge the dealer for it. A hard start is an assessory that is availiable with most units new or old from the manufacturer. They are needed many times for voltage variances. I would thing that if one was added and the system is working properly you shaoul be just fine. I also understand your concerns but this is when you need to rely on your contractor to do the right thing for you. If you don't trust there advise then I would try a different contractor.