It may be useful to consider what the throttle and elevator actually control.
Throttle (to a very close approximation ) controls the rate chemical energy is removed from the fuel tank and added as mechanical energy to the aircraft.
Elevator sets the Cl and Cd, changes in which generally exchange kinetic and potential energy. This also changes the rate of energy dissipation. For many speed ranges this is a rather marginal effect, however well above or below best glide, the effect can be very pronounced (I.e energy dissipation at Vy, Vbg, Vx will all be much much lower than Vso-20%)
The kinetic energy can be exchanged most quickly but is generally most limited in supply.
My instrument instructors tended to teach the lazy mans approach of trim for the air speed you want, use power to adjust your overall ROD (energy dissipation rate in this case), use small elevator input to address short term transients in energy dissipation (I.e. a transient move above GS due to a gust or air column off the parking lot)