I don't know how you guys with CT on can fight with flaps down. The CT fights against the flaps strangely in the 109 especially, making you have to press the stick forward in order to maintain your shot, and it's progressive I find as well, the more flaps, the more you have to compensate, making shooting much harder, with the nose bouncing around. As soon as CT is off, this goes away for the most part, or at least if CT is off prior to dumping flaps, it doesn't begin nearly as much. I find this to be at its worst when I'm nose low, for example coming over the top of a rope, with flaps full, target floating below me - with CT on during this time, the nose keeps trying to "climb" above the target, and this is where I end up having to push back against it, greatly and negatively influencing my aim and shot. If I come over the top with CT off however as I'm dropping the flaps, it's much, much easier for me to shoot.
I fly around with CT on some of the time, but have buttons on my throttle/stick to quickly turn it off and on, plus trim on one of my thumb hats on all my stick set ups. Fighting the 109 this way is much easier for me, as soon as I start to maneuver with another aircraft, I push off CT, and instantly put in a notch or two of down trim, so I'm pulling instead of pushing for my shot in the front view if anything, although usually it's pretty neutral and I don't always need to do it depending on speed and altitude. If I find myself way out of trim shape in a fight, I can always just quickly hit the autotrim again in order to trim out the 109 for whatever speed and position I'm in at the time. Once the fight is over, if I'm alive still, I just put CT back on and continue on my merry way, flying around without worrying about trim.