Not sure I'm with you there. The act of trimming the elevator only resovles the difference between turning moments created by the lift vectors of the stabiliser/stabilator and the wing. Basically you're changing the effective angle of attack on the tail to maintain a given attitude. A change in power will only necessitate a change in trim for a given airspeed if the tail plane generates more or less lift, which would require a change in relative airflow - the primary change of this comes from either the slipstream or from a change in trim
.
So if the tailplane lives outside of the slipstream the aircraft ought to settle at the same airspeed as it was trimmed for at any power setting. The tomahawk does this beautifully (as does the T tail arrow). The Jetstream does this really nicely as well
although I haven't really had the opportunity to investigate all it's characteristics.
The application of power will ultimately lead to a pitch change but not necessarily a speed change or a change in RoC/RoD it depends very much on the design and position of the tailplane and the trim system.
this is of course my opinion
and not necessarily correct.