Nope you are not asking too much.

Check your stab incidence. Downlines are mostly in the wing/stab alignment, not thrust. Assuming the stab is fixed, you'll have to keep dialing the wing, or live with it.

This is assuming your CG is correct of course. The flying CG should always be the first thing established.

Check the stab incidence first. If it's off tremendously, you could be fighting a losing battle.

You may also have a warp problem. That's not unheard of. Check that too.

Lastly if it has fixed gear, make sure the gear are not mounted at a positive angle relative to the flight path. This can also play havoc with trim in some cases.

Check all of that and see how it goes.

-Mike