OK, silly suggestion but why not add up trim to achieve level flight? But assuming you did this and trimmed for level hands off flight at some point then what are you doing to produce the pitch down effect?

Also if you trim for level hands off flight at mid to low throttle and then dive the model and release the controls what happens? This is the dive test that you can use to set the best CG for your model. Dead nuetral won't pull out of the dive or tuck the nose. CG forward will make the model pull out of the dive. Cg aft of the neutral point will make the model tuck under. Most folks trim to slightly positive or perhaps right on the neutral point.

Any model with some positive stability will try to pitch earthwards when inverted. If your model is doing that then it tells me the model is positively stable and you just need to add forward stick pressure for some down trim to get the elevator to mimic the upright position when inverted. It is this part combined with the upright nose down pitch that has me asking if you are trimming for level flight at mid throttle as well. Please pardon the presumption of something so obvious but since I don't know what flying background you have it seems like the right thing to ask with what you gave.