Honestly I think the OP’s “concerns” are way overblown. The fact that his Honeywell commercial thermostat along with his furnace’s built in safety overrides both failed and heated his daughter’s room to “over 120 degrees” (which by the way I highly doubt was the actual temperature, as things would have been catching on fire in the basement at that point, but I’m digressing) is a tragic accident, yes, but it tells me two things:
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Someone wasn’t having their HVAC system properly inspected and maintained. A competent installer should have been able to see there were problems with the safety features.
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Honeywell is one of the largest manufacturers of HVAC equipment in the world and, while once a maker of quality equipment, their consumer stuff is now built very much to a budget and I suspect by the absolute lowest bidder. Doing research and buying a good thermostat with safety features would have gone a long way.
The warning was about a commercial system failing and has absolutely nothing to do with building your own. As long as you do your homework and understand what you’re dealing with and the potential for things to go awry (and methods for preventing it), you should be OK. In fact, assuming your furnace’s safety features are working, I’d be much more concerned about building anything that plugged directly into 120VAC than I would building my own thermostat.
Just to stress, I’m not brushing off what happened to the OP, I’m sure it was tragic for him, but I don’t think the lesson here is “DON’T EVER TOUCH YOUR THERMOSTAT!” so much as it is, “Buy a quality, well reviewed thermostat and have your system serviced every year by a qualified and competent professional.” If you’re building your own thermostat I think you’re past these points and the message should be, “Do your homework, know what you’re dealing with and what can go wrong.”
Just my two cents! 
(As a side note, the OP mentions reading about a lady who went on vacation and when she came home everything made of plastic inside the house was melted. There is absolutely no physical way that’s even remotely possible. I’m sorry. Just, no.)
@jonathan That’s a bit overkill, really. Just use a bimetal switch! That one is normally closed (conducting) and will open (stop conducting) at 86f. Just put that between the output of your heat relay and the wire going into the wall. Get another one that’s normally open (not conducting) and set at least 10 degrees above freezing to put between the 24VAC feed from the wall and heat wire going to the wall.
With these two bimetal switches, the heat will cutoff if it gets too hot (86f in this case) and come on if it gets too cold (above freezing). This prevents your dog from catching on fire and IKEA furniture melting if your Core CFODs and the heat sticks on, plus it keeps your pipes from bursting by keeping the house above freezing if your power goes out or something. (That’s the beauty of bimetal switches: 100% mechanical!)