All aircraft respond to thrust changes (throttle) with a change in pitch (elevator).

The one item you did not mention is are you trimming in down elevator in response and does that help? Also can you fly at a steady reasonable power setting and trim the airplane so it hold altitude?

There is always the possibility that you have a small incidence problem.

So can you trim the airplane for level flight at a fixed power setting and does that result in a lot of down elevator from a normal intrail position?

John