I finally ended up with a design. I'm going to go for a small PCB that will mount directly to the solid state relay.
Circuit will feature a 3-input gate, inverters, protection diodes and voltage dividers.
Basically, there will be 3 inputs, and the board will be "hardware programmable" to activate the relay according to the inputs. Inputs will be for (1) the signal from HQ for low temp, (2) the signal from nest requesting heat and (3) from an optional microcontroller that could be connected to the cloud (though I'm not going to prioritize this feature for now).