No actual experience yet, as I am still rehabbing my first property, but... I'd be very concerned about leaving my property for too long without heat. Yea, my tenants could stay with a friend, or I could put them up at motel, but the pipes could freeze. I plan on bringing my oil-filled space heater over immediately, and calling an HVAC company as soon as feasible, if/when I get this issue. (Wish I had your skills & knowledge Jon :-)
Note, I have run this oil-filled space heater on a timer for the past six or seven years to heat the 'bunny room.' (Spoiled bunnies.) The timer uses little pins that can be pulled completely out, so I bought extra timers to get the pins. The space heater runs for about two hours, is off for about an hour, runs two hours, is off again, you get the idea. This is to keep the power cord from getting too warm. Haven't had an issue.
Of course, the pipes in my tiny little two bedroom rental property could probably be heated with just two of these heaters. A normal house might need a dozen!