It depends, partially on what you precisely mean with "trim".
Pilots use a rather narrow definition where trimming means to zero the control forces for a specific control surface deflection and speed. This is achieved by tabs or springs in the control linkage.
Engineers use it more broadly and include the ability to deflect control surfaces such that the desired attitude can be stabilized. I guess that you refer to this line of thought.
Long before the lift coefficient of a stalling airplane peaks, the flow over part of the wing will start to separate. Ideally it will do so near the trailing edge of the wing root, and the separation will slowly progress forward and outward as angle of attack increases. This separation will shift the local center of pressure back, such that the aircraft will experience an increasing nose-down moment as it approaches stall. To stabilize it at higher angles of attack will, therefore, need nonlinearly increasing elevator deflections. Depending on the position of the center of gravity, the installed elevator authority might not be sufficient to trim the aircraft all the way into the fully developed stall.
If you mean the first interpretation of "trim", then yes, most aircraft will not allow you to zero stick forces into the stationary stall. The trim range should cover the speed for steepest climb, not more. However, if the center of gravity range is wide enough, you should be able to trim an aircraft with rear c.o.g. all the way into the stall. After all, with neutral stability you can ideally trim (second interpretation) any angle of attack with the same elevator deflection angle (note that the nonlinearity explained above will require more negative elevator deflections as you approach stall even in a statically neutral aircraft).
I would rule out that the control forces are too high - after all, when stalling in level flight at 1g the aircraft will fly as slowly as possible, so stick forces should be small.
The effects of thrust depend on the engine installation. With a propeller, more power will add torque and increase the dynamic pressure at the tail. Now it depends whether the prop blast will hit the empennage - if it doesn't, the effect of adding power will at best be be an asymmetric stall.
In case you have a configuration change where the older configuration is known and the new should give the same flight characteristics, use tail volume as a sizing parameter. Horizontal tails of the same volume should give the same control power. Volume is the product of area and the lever arm between tail neutral point and the center of gravity. If the new tail has a different dihedral angle, don't forget to add the cosine of the dihedral angle.
When comparing elevators of the same size but of different flap chords, use the square root of the relative flap chord for comparison. Say the old elevator has a 20% flap and the new one 30%. The new one will have 22.5% more control power for the same deflection ($\sqrt\frac{0.3}{0.2}$).
Depending on elevator chord, at some point more deflection will not help much (typically 20° for a 25% elevator - going higher will add little control power). Now several options can be employed to increase control power:
- Change the incidence of the stabilizer. That is what airliners do to compensate the massive trim changes caused by Fowler flaps.
- Add leading edge devices on the stabilizer to make the elevator more effective. This adds a lot of complexity for a small gain, however.
- Use slotted flaps and double flaps to eke more control power and higher useful deflection angles from an existing elevator. Again, airliners with their wing flaps should point the way.
In damping, both the dihedral angle and the lever arm have a quadratic influence while they have a linear influence on control power. This way one can adjust damping and control characteristics individually.
