Does this seem like the right place to tap a C-Wire from my heater?
We've seen exactly the same wiring diagram.. with almost the same question asked.. over there: Where to connect C wire if no C terminal. But you've found additional information about the appliance controls!
It looks like the pin 6 you've identified is not always-on 24V. Instead, it is the switched line coming from the thermostat's call for heat.
The text from the service manual does lead one to believe that pin 5 is the common terminal you're looking for. You can confirm it with a meter by measuring voltage from pin 5 to the R terminal, or you might consider the answer I gave on that other question.