I'm putting here two photos of the transformer, please consider that it's not how it was originally setup: I've separated some of the wires (I explain why down below).
The way I understood is like this: originally, the transformer has the primary neutral connected to the secondary neutral and then you have 3 pairs of windings that will generate 1/7 (+15V) of the main voltage (+110V).
I believe this exists because, depending on how you use your relays, you can use the first two pairs of windings (let's call them A and B) to increase the voltage by 1/7 or decrease it by 1/7 so you can regulate if there's too much voltage or too little coming in (thus stabilizing the secondary output).
The third winding (let's call it C and also with a 1/7 ratio) is used for the electronics part, so it gets rectified, filtered and used for the microprocessor, comparator, controlling the relays, etc.
What I did was identify the neutral wires and separate them (so I can have isolation) and then used the two first pairs (A and B) as my isolation transformer's primary and secondary --> I've put 6VAC on one of the pairs, resistors on the other pair (to limit the current and ensure the voltage is not ghost) and got around 5.7VAC in both pairs of windings (isolated). The third winding also get's 110V but I'm simply ignoring it.
The problem is that the original winding (that in the original configuration was the primary at 110V) has 7 times more voltage because simply of the number of turns --> I get around 40V on it when I put 6V on one of the other pairs.
If I put the whole thing on 110V, this will generate 770V in that winding.
As you can see from the picture, the wires are beefy and most of them are doubled, so I don't see any issues to handle big currents, but perhaps I'm missing something: what do you think?