Really, this is my worst nightmare. I have a quartz heater in my portable now. The oil/electric one apparently burned the electric cord right through. I was EXTREMELY lucky that it did not come to what you experienced.
I am guessing that because it was soooo cold the heater just went full blast and got too hot. This may be what happened to you all.
The quartz one, they are HARD to find, has a cutoff if it is overturned and a safety caution if the wattage is too great and it turns itself off.
I fear it will turn off on a really cold night, so I installed a electric temperature monitor and a red light comes on in the window if the space gets below 40 degrees.
OMG, Good Luck and I am so sorry you lost your chickies.