...we also know that each wing is producing the same amount of lift. However, there's no reason why two different aerofoils operating at two different angles of attack should also produce the same amount of drag,...
Yes, I agree with your line of thought. The point, I think, is that it's a second order thing.
Looking along its span, the aileron-down/upgoing side produces mostly a little less lift and then, close to its tip, much more lift. The aileron-up/downgoing side produces mostly a little more lift and then, close to its tip, much less lift. Because of the shape of the drag/lift curve with aileron deflection as a parameter, the latter is more efficient (less draggy) than the former.
It is mainly a TRANSIENT phenomena. If it wasn't, the aircraft would continue to yaw during a continuous aileron roll until it was flying sideways!
To accelerate the aircraft in roll does require a difference in the lift that is produced by each wing and hence the difference in drag experienced by the wings, causing the adverse yaw to begin.
I'm not convinced that it's a transient thing. Roll damping has a typical characteristic time of the order of 0.1 sec. That means that if you apply aileron very abruptly and start accelerating it in roll, you reach steady state roll rate in about 0.2 sec. I think that aileron drag persists longer than that, and is pretty much dependent on aileron deflection.