There are several advanced methods for fully trimming a plane (I like the "Peter Goldsmith" method). You can google it to get all the details. But for a quick, rough setup:
1. Fly at about 3/4 throttle or above. Trim it so it stays straight and level.
2. Pull and climb at a 45 deg angle. Roll to inverted in the climb. Do NOT touch elevator or throttle. While upside down, if it pitches down, it is nose heavy. If up, tail heavy. Repeat the test several times to verify the behavior. A bit nose heavy is fine. Serious 3D guys will want it to neither climb or dive in this test. Adjust CG, and test again, until you get it to just slowly pitch nose down.
3. Now try your high/low speed testing. If it still behaves as you noted, shim the engine to give more down thrust.
4. If that helps, test for CG again. The change in thrust can mask the CG effect a bit, so reverify and correct again if needed. If you did have to correct, try your fast/slow test again.
Purists will note that some of what you describe is normal, since speed generates lift, and one then has to trim to compensate. But what you describe seems excessive. Hence the shims.
If you have to go more than a couple of washers, as advised above, check the relation of the incidence of the wing to that of the tail. Something there may be way off.
Last edited by tedsander; 05-26-2021 at 08:37 PM.