Mine is not like that at all.  I don't know what the problem is but it certainly isn't a design one - its a great flying airplane.
I have my CG and throws set per the manual and that is fairly nose heavy IMO.  I needed a lot of nose weight to get to where they suggested.  I plan to move mine back next season (flying is done here for the next few months.)

The only negative thing I have noticed with mine is that it's tricky in a cross wind landing due to the large size area.  On slow landings you need quite a lot of elevator to flare.

I have a Rhino in mine - I adjusted the position of the engine to stop it climbing under acceleration.  On a P120 it should not climb under power.

My ailerons are not set level with the flaps - they are set so the ailerons are level with the wing tips.  That means the flaps are slighly lower (about 2mm.)

Any chance you have some binding on the elevator mechanism?  It almost sonds like something is moving inside the airplane for things to be as drastic as you described.  My airplane is ROCK SOLID in the air, not pitch sensitive at all, no bad habbits at all and very easy to fly.  There is definately a problem somewhere.