Update on this problem. Our York heat pump system is working great. Our utility bills went down and (so far) we are satisfied with the system. No more run times lasting hours or shutting off for a few minutes only to restart again (like with the Amana). The system has worked great this summer and we have had EXTREMELY high temperatures this summer and our cooling bills have been manageable.
The company that installed the systems say they are no longer installing Amana or Goodman systems any more because of the problems they were having with them and the lack of support from Amana. I know they were extremely frustrated with Amanda when they were trying to figure out what was going on with the two systems they installed in our house.
Sounds like a cop out answer, BUT I'm glad your issue has Bren resolved!