I like the idea of adding your own winding, but, 2 turns per volt sounds a bit optimistic.Wind on a small overwind of about 24T for 12v.
I have rewound and also added overwinds on many different transformers over the years, the EI type I found was up around the 5t/volt, but Toroidal I have found as low as 1.5t/vI like the idea of adding your own winding, but, 2 turns per volt sounds a bit optimistic.
For a small transformer I would expect 5 or 6 turns per volt, so you would need 60 or 70 turns to give 12v.
If you don't exceed the current rating, you can use a transformer at a lower voltage.
If you have a 30 VA 110 V primary 55V secondary transformer that can supply 0.5 A, so it will be fine converting 24 V to 12 V and supplying 0.5 A.
It will be much larger than if you got a transformer wound specially.
How many do you need? Is this to run at 50 /60 Hz or is it some other frequency?