Written off & on over hours(if its been said, sorry)
Brianel-A low power draw coil, from an add on relay, could be powered from that dc units board, then introduce AC on the relays points. A relays linear motor(sol. coil) uses dc well, and uses less power than a rotary motor most often.
How do you happen to own "pic E"? Was that part of the whistle shed? What is the part number for your shed. You do have some experience obviously, but how much you know is still a bit of a mystery so...
Assuming your using a conventional Lionel ac transformer.
You need the modern equivalent of a whistle relay first, a whistle relay board! It ignores the equal pos/neg waves (like on an oscilloscope) of AC volts normally on the track, instead its triggered by a "DC voltage offset". An increase in just the positive ac wave (or negative for a bell) gets used as the relay trigger. A D cell battery touching the ac powered track will trigger it (but don't long term, batteries of the 1950s were made different, a little ac to them was ok. Exploding alkaline, etc. is bad.)
These modern board type relays aren't always easily triggered by PW transformers because they still use the whistle rectifier disc, and issue a smooth wave on a Osc. scope (full sine wave). New stuff "chops" the wave up, because what it does, happens so fast. Those smooth waves, look like steep cliffs now. Visa versa, modern sound buttons, not inside a transformer, don't supply the 5v boost the transformers do, to start the old whistles moving. The older whistles need a quick 5v boost and the dc offset(1.5-2volt) for whistle, new ones do not. That 5v is the speed up you see when you hit the button. The principle is the same.
Your old transformer could be updated with a large diode to do the same job as the disc. It will operate newer items much better, and leave in the boost for the old stuff.
The wh.motor you have now is likely dc, so the tracks ac must be converted to dc before reaching the motor. Or the relay board may change it to dc.
Point is, once we figure which trigger to use, we need a reading off the Wh. relay board, to see if its ac/dc/ or a switch happening to the outputs.
You have sound buttons, I can read a diagram, but I have not used either Part, so a part number would help for everything and/or where you got it.