You've done a good job of documenting the problem. I'd put this information into a letter form and then ask that the unit be replaced - under warranty. Send copies to the CEO of Amana and everyone else all the way down to the owner of the company that did the original installation.

I know very little about heat pumps, but I know that you should not be having all these problems. The first problem with the "hard start" kit is a big red flag. Those are typically installed on old compressors that are on their way out. "Hard start" means just what it says - the electric motor is old and needs an extra kick of electricity. It's unconscionable to put one of those on a brand-new unit.

Rose

We have a heat pump, and so far in 13 years, no issues except getting the coolant refilled... easy peasy.. so far.
I Hope you can get it fixed quickly and reasonably..

Our old unit was a Trane and had no problems in the 12+ years we had it. Didn't even get it serviced like we should have. Replaced it so we could lower our energy bills with a more efficent unit. It does that - when it works!