From what I've heard, using a reptile heat mat is extremely unlikely to overheat, I'm not sure what temperature it would reach if it did though, so I'll look into that.
I used to sell exotic animals for a living, I'm very experience in reptile heaters... I have seen many overheat and fail, I have even seen them smoke up and melt... Plus as I said they are designed to run at +20° over room temp, thus in your application they are likely not going to work unless your coop is always 80° or more, combined with the fact they are slow to heat and recover...
Also, reptile heating pads are usually placed directly under the terrarium, they have no issue being covered by it that I've ever seen or heard about. I could test what temperature they can keep a nesting box at at some point.
You described their use outside the tank on a sheet of glass not covered in combustible bedding, or worse a layer of combustible chicken dust and feathers... Go read the warnings, even the ones that do say you can cover with a 'thin' layer of bedding warn it could cause failure of the unit...
Do you have any alternative heating method which could be used?
Nothing that doesn't run a fire risk, beyond some type of hot water radiator or forced air system with the heat source outside the actual coop area...
Also your idea for a pressure plate is prone to fail as well, dust, poop, feathers or what not could cause it to get stuck on or off or not function properly...
BTW, I'm a freelance electronics engineer, I brain storm and design things like this for a living.. I'm not trying to flat out negate your ideas, I'm simply pointing out factual issues and concerns with the design...