When I mostly flew an Archer, I did the same. Somehow in the transition to the
Mooney, I've becomre more fixated on the AI. Not sure why.

Because the Mooney demands more precision in your attitude control.
The cleaner the airplane, the more true that is. Once you reach the
ultimate clean airplane (a transport jet), there is no way to fly
partial panel. No jet crew that lost all attitude indicators in IMC
has ever survived. That's why the airlines have given up on teaching
partial panel. On the other hand, an old, slow, draggy ragwing can be
flown with no gyros at all, using just airspeed (or sound) for pitch
and compass for roll. I know someone who has over an hour of IMC time
in a ragwing with no gyros at all, doing it exactly that way. I've
done it at night under the hood in the TriPacer.

The Archer was so stable it was easy to follow along just using the
result-based instruments. In the Mooney, it became necesary to be more aware of
slight changes in attitude that would affect the performance instruments in a
few seconds.

Exactly correct.

This is why I teach the control-performance model of the scan - my
students are generally either flying slippery airplanes or are planning
to move up to them. For someone who will fly his entire career in an
Archer or Skyhawk, the FAA primary-secondary model works fine, and then
the AI is just a way to crosscheck.

Michael