Well, I'm done for now:
-- Having concluded (along with the consensus of responders) that it would not be possible to get to the motor and gearbox driving the defective fan animation and effect repairs without serious damage to the piece, I resolved to kill the power to the (very loud) motor. A careful inspection revealed two single color-coded wires running to the motor enclosure, amidst a number of joined wire pairs, so I took a leap of faith and cut one of the two wires (at arrow):

Voila! The motor was disconnected, and all lights are still on! For those who have found the motor noise objectionable, a simple slide switch could be inserted at the break to allow turning the fan animation on and off as desired.
-- The next modification I made will allow the piece to be run directly on accessory AC (which is available from multiple terminal boards under the RFC train garden layouts), rather than a Menards 4.5 VDC power supply. The piece has both a side wall-mounted female 5.5mm socket and an in-line female socket connected to a short wire underneath, presumably to pass through a layout for connection underneath. All I had to do was cut off the plug, check polarity, and connect it to the output of a buck converter set to 4.5 VDC (note: the piece can still use a Menards power supply through the side socket). I drilled a small hole in the base and passed through a two-conductor wire (putting a figure-8 knot inside to take up any strain) and connected it to the input terminals of the buck converter I secured inside, using two-side foam tape underneath:

Once installed on the layout, the wire can be passed through the top and connected below to the nearest accessory voltage.
-- The end result is a Menards (formerly animated) piece ready to power with the layout-standard 14 VAC, rather than requiring a proprietary Menards power supply:

If I can come up with a name more Cambridge-specific, I may attempt to replace the translucent and backlit "Vetter Sash & Door Company" sign, but for now it's ready for reinstallation!