Is there a way to make a thermostat based heating system more accurate through either adding probes or hacking?
The temperature probe is internal to the dial mechanism. 

Due to longer lag times of steam systems vs forced air systems, many steam thermostats have an anticipator setting which compensates by shutting the system off "in anticipation" of its reaching the correct temperature soon.  Research your thermostat brand online for this possibility.

Your real problem is one thermostat is attempting to average the output of multiple radiators.    A better solution is individual thermostatic controls at each radiator, but this solution must be designed from the outset for the whole building.  You should research whether you have a one or 2 pipe steam system.  

Steam thermostatic valves (google search)