If you can work at the component level, the below will work. I use it.
Rectfier to convert 12 vac to dc voltage.
Regulator for 3 vdc. If you have a 12 vdc on the power pack, forget the rectifier. I have gone both ways.
You can use the 5k pot but adjust for 3 vdc before connecting your other circuits. I prefer a dedicated regulator to avoid Murphy. Until you exceed 1.5 amps, the voltage will stay at 3 vdc.
The components are available from Radio Shack the last time I was there.
An old 9 to 15 vdc wall wart will be a good substitute for the rectifier. They are sometimes called wall transformers used for various electronic equipment,
Rich
If you ever fall over in public, pick yourself up and say “sorry it’s been a while since I inhabited a body.” And just walk away.
My guess would be that a board like that, in order to keep the price more reasonable, does not have any rectifiers or regulators for the input power. In other words, it's designed to be powered by 2 AAA batteries, and nothing else.
If my assumptions are correct, then yes, you will most likely let all the magic smoke out if you power it with 12v AC.
I am about to assemble the Walthers Arnold's Drive In Restaurant kit. It comes with a flashing sign controlled by a circuit board. I was surprised to see this flashing sign is designed to be powered by two AAA batteries rather than AC power. This kit will be installed in an area wear I will do a significant amount of lighting for night running and I had planned to hook up all this lighting to the 12 volt AC accesory power on an old power pack. My question is whether I could cut the wires to the battery box and instead power the circuit board from the AC power or would I risk overloading and burning out the board if I did that?