[EDIT: I'm not sure if this sounds like I'm trying to be difficult or anything. I'm not trying to be. Rather than re-type it I'll just add a comment saying "sorry" ahead of time.]
I don't think trim works the way you describe it lengro.
Trim just sets an offset angle deflection (it resets the default) based on your current speed. It is not constantly adjusting things for you, or dampening things for you, when you're in a knife fight. There's a table or chart that says "at this speed, deflect ailerons N degrees, rudder N degrees, and elevators N degrees." Then it just updates that chart periodically based on airspeed.
At worst, it dampens elevator authority in specific planes because it is trying to trim it one way and you're pulling the other.
I understand your request, but question the cause-effect relationship. Say you're set at "zero trim" like you just took off. You're fighting the plane more because it is out of trim, and more than likely are going to lose because you could not get your nose down in the right window for a shot, or were too busy fighting the wingtip stall to evade the bandit rolling into you from a rolling scissor.
Other than the minute amount of drag (so minute it won't effect a dogfight) what benefit does having "zeroed trim"* do? I'm not quite sure what the benefit is. Say you've zeroed the trims: You still fight the stick to get the plane to go where you want. Say you've toggled CT on and off: It's trimmed for your speed band, and if you get significantly faster you'll fight the stick to get the plane to go where you want.
Is the end result just fighting the stick, same as you do now?

*= in quotes because I don't know if that's the actual term