This may or may not speak to your problem, but when I did my initial instrument rating, my CFII had me doing so much partial panel work that I got in the habit of relying mainly on the VSI and turn coordinator for attitude control, even when all the instruments were available. When it came time to learn multiengine OEI approaches, I found that I had to pay far more attention to the attitude indicator in order to be successful. (I also had to get in the habit of keeping my course corrections small when flying a localizer.)
That is getting close to the problem. I figured out something today similar to this that helped me out.
And thanks guys for all the responses. I believe my problem is a combination of trim (too much overcontrolling as Bob mentioned), focusing on the wrong instruments, and going through the steps too fast when the engine fails.
Today, I tried an ILS approach with no hood (though still only focusing inside) and no engine failure. After getting set up and on the needles, I simply focused nearly all my attention on the HSI and the ASI. And it worked great, all the way down to minimums. Then I did the same on the next ILS approach, but the instructor threw in the engine failure this time. I then went VERY SLOWLY, focusing again on the HSI and ASI. I took deliberate, slow steps to feather, etc (all the usual steps) and just kept focusing mainly on the HSI with occasional glances at the ASI to make sure I was good on speed. It seemed to work much better, and with a strong crosswind today to boot - I think I was focusing too much on the VSI and altitude indicator before. I will try again next week and see if I can improve further.
One thing mentioned above was Rudder Trim. I had never touched it, and my school doesn't want me touching it during OEI training. I then asked a friend of mine who is a great instructor, and he said with piston twins he never recommends it. I then asked another friend who is a former examiner and he said the same. Soooo I think for now I will stay away from including rudder trim in the equation. I will say, this Aztec doesn't seem to need much rudder to split the ball during OEI approaches. During cruise flight with OEI, it does, but not when coming down under less than full power. This Aztec has a big-ass rudder, maybe it helps.
Thanks again guys, I'll keep you updated.