Moving the center of gravity may make the model to sensitive in pitch to speed changes.

I'd check the balance by doing the dive test thing. Dive the model at about a 45 degree angle with the engine at idle. With the controls at neutral the model should show do a very slow pull up to level over about 150 to 200 feet of altitude. That's about as close to neutral as I'd like to get. If you really want it neutral then sneak it back in very small amounts until the dive is dead straight so you have to pull it out yourself. Any sign of the dive steepening toward vertical is a sign that you're behind the neutral setup and that could be causing the nose up.

Once it seems good try the same test with the engine running at cruise to full throttle. That should point out any thrust angle problems. The pull out should be the same or just very slightly more positive with the higher speeds.