Okay, dissecting the $6.86 Vent-Miser was a snap. Literally. Everything is just snapped in place. 
And once it’s disassembled, the good news continues. If ever there was a product begging to be the base of a smart-hack, this is IT. First, as you can see in the Amazon product listing, the controller is just a little plastic box that snaps in and out. (Pretty clever design on several fronts, since programming as it exists right now wouldn’t be pleasant standing on a ladder with your hands over your head.)
Once you flip the unit over, a cover snaps off and you see that the little white box snaps into a receptacle that with two leads that feed the motor. The motor operates the louvers by a simple rack-and-pinion design.
You could always just gut the little controller box and replace its innards with the needed circuitry, assuming the needed circuitry would fit. If it won’t, there’s a lot of available room inside the shell on the back of the vent. The controller box is a simple design that could be easily replicated for 3D printing and modified designs.
So, for the more HA- and electronically gifted among us, what’s needed for this hack?