If it is truly a "very steady thing of beauty" upright, it should be the same inverted. The airplane and it's aerodynamics don't know what the orientation is in level flight. If it locks in and flies level without you moving your hand, then it should do the same inverted. If it does move, you are moving your hand trying to find a comfortable position and your mind is racing "up is down and down is up" at the same time. Some mild panic sets in and you over control. I don't call it a "hunt." Hunting is really caused by the before mentioned sticky controls, or some other type of misalignment, and some times pointy leading edges. If it's you causing it it's called "pilot induced oscillation." People are always more nervous when flying inverted, especially in their early stages of leaning the pattern. You are in your early stages of learning the pattern and trimming models, and if you ask the question here on the list, then you will have trouble determining the problem in real time. Your best bet is to have a genuine expert class flier fly the airplane and have him feel out the model in inverted flight while you watch. You have to come up with your own style of doing the maneuver that makes you feel comfortable so you can relax while flying that six laps. Some guys hold their hand like normal, some lay their hand over on it's side and everything in between. Laying your hand over on it's side can cause issues like you describe, especially if you can't "lead" the airplane properly to keep the up and down line tension the same. Easy to do when the handle is upright. You are probably flying like this when you fly inverted. And you are best to keep the control direction as "top control" and "bottom control." No matter what the orientation of the airplane, the top is always the top and bottom is always the bottom. You give the control movement in the direction you want the plane to go. I guaren-damn-tee you that is you were flying Dave Fitz's own Thundergazer in this manner, you would probably still get some "hunt" while flying inverted. If you can not fly inverted correctly yet, then you will never trim a model into it. if it was that rock steady and solid, it would NEVER turn a corner!
I'm Just Sayin',
Dan McEntee