Okay... After reviewing your new photos, I think I have it figured out. 

This is what your system looks like

![Boiler wiring][1]  
<sup>*You'll have to excuse the glitter pens, it's the only thing I could find on my wife's desk.*</sup>

It's pretty simple actually. When a thermostat calls for heat, the valve for that zone opens, and the boiler is also signaled via the auxiliary switch in the valve.

To get a `C` wire to one or more of the thermostats, you'll simply run a wire from the other side of the transformer on the wall.

![New boiler wiring][2] 
 
<sup>***NOTE:** If this diagram is accurate, the white wire to the thermostat is `R`, while the red wire is `W`.*</sup>

The original wire from the transformer should be connected to the `R` terminal on the thermostat, while the new `C` wire should be connected to the `C` terminal on the new thermostat. This should supply power to the thermostat, and allow it to operate as normal. 

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I'd like to see the wiring at the thermostat as well, to be completely confident in this answer.  Though it makes sense now how it works, so I'm guessing this is fairly close to how it's wired.

  [1]: https://i.sstatic.net/ymgjw.jpg
  [2]: https://i.sstatic.net/q5qK8.jpg