This sounds like what my parents went through- who live in northern MI.
so here's the story- My father is a retired pastor and they live in an area hard to get repairs(the reapir man did not know he was a pastor). The repair man was vage and not particularilly helpful the first time but willing to collect payment. My father discovered later there was a crack internally on the furnace and called the man out again who was reluctant to come claiming (blankity blank blank) it had been fixed. As the man begrudgingly got down on his hand and knees to check things out my father put his hand on the man's shoulder and began to pray- Lord we thank you for this man and the skills you have given him. Now Lord we ask you guide his hand and help him be able to find the problem ( something to that affect). needless to say the man was a bit taken back and his tone changed drastically.
Ther furnace also came form a defunked company but when they spoke to another company and expalined their dilema they offered a good discount.
In the mean time they hung a plastic shower curtain across the entry to the living room and ran an electric heater which really kicked it out.
Sorry for your dilema.