Home Warranty of America No heat and needing new furnace; "too bad" says HWA. You have to wait. Internet

We purchasd a home in September 2015 (3.5 months ago), and because the home inspection report stated that many of the items (furnace, hot water heater, et. al.) were at the end of their expected life, we had the former owners pay for the home warranty.  All was sort of okay, until the furnace died.  We had used the furnace for a couple of weeks at the beginning of November and right before Thanksgiving, it died.  We had scheduled a maintenance call the day after it died the Wednesday before Thanksgiving.  The HVAC folks doing the maintenance, stated that there was really no way to fix it; the entire unit (heat pump) and compressor needed to be replaced.  We had to wait for the HWA vendor to come out to check it the same day, and he said the same thing - it needed to be replaced completely.  So we went to stay with my mother - 3 hours away.  We called HWA in the car on Friday and kept calling - their vendor had not filed the report yet, so we had to keep waiting.

  My husband is 69 years old with diabetes and I am 63 (we are now considered "elderly"), and the house was down to 53 degrees at this point.  HWA said we had to wait until their contractor could file his report.  We took the decision to have it replaced - what were we supposed to do at that point?  It took until Monday, when they called back (now since Wednesday before).  I told them I wanted to cash out this part of the policy - and they offered approximately $970.00.  The new system cost $6,700!  I asked them where they could purchase a new furnace for that amount.  The response was that they were going to try and fix it first (even thought 2 HVAC specialists said there was no point), and that we would have to wait for parts to be ordered and then they would see about fixing it.  Seriously??  This is a complete rip-off and I cannot believe that they expected us to stay in a cold house with no heat for more than a week, whilst they tried to order parts for a system that was more than 30 years old, and we were supposed to live there.  This is unconscionable and they need to repay us the cost of a new furnace system.