I guess I would start by flying the plane up to a comfortable altitude with minimal fuel and then chop the throttle completely to 'OFF' then let the plane glide down and see what is happening with trim. If properly balanced and the angle of the stab to the angle of the main wing is acceptable the plane should make a smooth, stable glide at your chosen landing/gliding speed. If a handling problem is still observed then we can eliminate the engine thrust from the THIS problem because there is no engine thrust.

If the plane glides/lands without any major flight handling concerns then I would focus on the thrust vector of the engine.

If the engine is OFF and the plane keeps nosing up with increased glide speed look into the center of gravity or the wing angle compared to the stab. I would expect that in the glide, if you add a little nose down then release the stick, the plane should not nose up on its own (This would be similar to the 'dive test' for sailplane CG testing).

My gut feeling is that there is excess wing angle compared to the stab and when the engine is above medium speed the engine is pulling the nose DOWN thus hiding the problem. When the engine is slowed then the adequate downthrust is no longer present and the excess lift produced by the wing takes over.

I would think that if you eliminate the engine thrust completely and have the center of gravity set adequately and you still have a problem then the only thing left to look into is the angle between the wing and the stab/elevator.

I would not create a more powerful stab force to solve the 'symptom' of the problem. That would not be a long term or proper fix in my opinion.

If you are thinking that the downwash of the main wing is stalling (or actually 'blanketing') the stab at a specific speed and angle of attack during landing ... hmmm ... that might be worth looking into.

This might show up in the glide mode noted above by starting at a rather steep glide then very gradually slowing with increased 'up elevator' and watching the plane for a 'change in handling' at a certain 'nose up angle/speed' combination that might indicate a 'downwash' interference beginning.

I recall that Bob Dodgson (of sailplane fame) installed a 'trip strip' on one of his 'modified' planes (a Camano?) with which he was having flight handling problems after introducing the modified location of the stab placement on the fin. He noted an improvement in the handling with the trip strip installed. He later concluded the trip strip changed the airflow over the wing and prevented the stab being affected as it had been previously. Thus he determined that the 'modified' stab location was not the proper location for use with an 'untripped' wing. Maybe you can try this on your plane since it is very simple to install a trip strip, run some tests then remove it later. I believe for his wing the trip strip was .020 inches thick and 1/8 inch wide (multiple layers of some type of tape) and located at 20% of the wing cord and placed across the entire wingspan.

Another area to investigate may be the settings of any flaps (if they exist). Possibly the flaps can be raised to modify the downwash of the wing and observe if there is any change in handling during landing.