First, keep in mind that engine thrust line, wing incidence, stab incidence and balance point are all related. A change in one will act like and/or effect the other.

I’m not sure what other planes you have flown, but be aware that more aerobatic models require almost no down elevator when inverted. Compared to a trainer, it will feel very different. The ideal setup for most is just a breath of down elevator to maintain inverted flight.

You mention two problems. Climb while inverted at neutral elevator at idle, and pitch to belly at knife edge.

A climb while inverted (at idle) can be caused by being tail heavy, not enough down thrust, and too much wing/stab incidence.

A pitch to belly at KE (assuming high throttle) could be caused by tail heavy, too much down thrust, and too much wing stab incidence.

You are carrying up elevator for trim, which would explain the too much stab incidence. The question is then why that much? Something else if off requiring you to carry up elevator trim.

Pitching issues like what you mentioned can take awhile to isolate. My suggestion would be to use a trim chart, such as can be found on the NSCRA web site at http://www.nsrca.org/trimA.htm

What I would first check is CG. Be 100% sure it is where it should be. You may need to tweak the CG later, but recheck it is as per the plans.

Next check that the wing & stab are both at the same incidence. Be sure to check this with the elevator retrimmed to level with the stab. My guess is you may find a problem with the stab. Do your best to verify they are at 0 compared to the datum of the plane, but this may be difficult to judge.

Then check thrust. At WOT in level flight, chop throttle to idle. The plane should slowly arc down as it slows. If it climbs, you have too much down thrust. If it sharply arcs down, you have too much up thrust.

Next, put plane into a straight down dive at idle. Be sure you are high enough to get into a 5+ second dive. It should continue straight down. If it pulls out, you don’t have enough wing or stab incidence. If it tucks, you have too much.

You may have to go thru several trials & changes until you isolate and solve the issue. It is not uncommon to require 20 or more flights to setup aerobatic trim on a model.