Thankfully, these roofers were able to make repairs to the house roof quickly with little difficulty. Unfortunately, the garage roof was a different issue. Because the damaged exhaust vent led directly to our garage's gas heater, the roofers were not licensed or insured to make those repairs. Thus, I had to get ahold of a heater technician to see what he could do. Ideally, we wanted the heater to have its exhaust go out the back wall rather than up through the roof.
The heater technician gave me more bad news. Likely from water coming down through the hole left by the broken exhaust pipe, our heater had several cracked elements and was no longer safe to use. The good news was that the technician said that a new heater could be installed that could vent through the wall. Thus, we removed the exhaust pipe, and I had the roofers cover its hole entirely as part of the garage roof repair.
Today, the heater technician returned and installed the heater. It was then that we discovered that the exhaust could not go out through the back wall because it was too close to a window. Instead, he had to put it out the side wall ... so that the exhaust pipe would be in the direct line of attack from snow falling off the roof. I requested that he put in an elbow and have the pipe follow the wall out the back. He did so only under my insistence as he is concerned that the pipe could have condensation freeze up at the joint and have ice slowly block the exhaust.
We will have to keep an eye on it this winter.