Hi there,
I have been taking a look through this section and noticed your porblem with your concerns of overheating the metal core and windings of the transformer.
If you get it right, the windings will run happily with little stress, however, nothing in this world goes according to plan, so build in a safegard to cool your transformer.
I suggest you take apart the charger and mount a cooling fan (use a computer fan)facing the core windings, so it is blowing right at them.
they draw very little current at 12V DC, you can also control the speed if required.
I have a backup DC power supply in my house, consisting of two medium size 12V vehicle batterys, I have them on a constant trickle charger modified cooling with a PC fan.
It has been working without fault in up to 40 degrees celcius without problems.
I also did the same with an old UPS, I put a LAPTOP fan in it, reducing the voltage with a LM7805 regulator. Before the windings werte to hot to touch, now it runs cool.
Again, when delving into the insides of high voltage, take care with what you are doing, if you dont know how to modify properly, then stop right there and get someone you know who knows what he is doing. TThis is for those who might happen to read this, you know the type, over confident persons with no knowledge of electric power and wouldnt know what the active and nuteral was about.
Good luck with your transformer conversion