Very interesting - thank you for doing this!
I believe this thread (and all other threads I've found online for that matter) has missed one important part of the schematic with regards to T210/C210 compatibility.
Analog switches controls what signals feed the differential amplifier. When SW1 and SW2 are ‘0’, T_TIP represents the temperature by measuring the small voltage between TC and COM. The circuit is at this state most of the time. One time during power up and one more when the handle is connected, the circuit changes SW2 to ‘1’ during 30 ms. At this point, both inputs are connected to TC. Maybe this is used to see the offset of the amplifiers. Sometimes, especially when the tip temperature decreases, SW1 goes to ‘1’ for 300 us up to 8 ms. Now the amplifiers are measuring between LOAD and COM, this is the voltage drop at the heater.
The one remaining combination is LOAD + TC when SW1 and SW2 are both 1. I believe this will be used for T210 handles as the cartridges are wired differently (LOAD and COM are swapped), so you likely didn't run into it with your testing with a T245 handle. This is fascinating, as in other threads (and earlier in this thread) the general wisdom is that for C210 cartridges the heater and TC have no common tap between them, so every open source JBC T210/C210 controller I've found is powering the heater through the TC (and likewise measuring the TC through the heater)!
Here's a diagram I found in the Unisolder thread over at the Dangerous Prototypes forum. Of note is that the T210/C210 connections do not match anything else that I've found online, however they fit the circuit here as I've described, and more importantly all my C210 cartridges appear to corroberate it. Having said that, I haven't actually hooked the cartridges up to a TC amplifier yet to be able to measure it.