PuppetZ, I think I understand your situation, which is a stage that everyone goes through. To your specific question the real answer would be that there are way too many options to go through one by one, but that will not be very helpful.
Basically, in the situation you describe there are two main paths you can choose - one is to go for the snap shot and extend, the other is to completely give up the shot and try to reposition. What ever you choose to do, and this is the critical part, you have to choose early and follow through with it.
Going for the snap shot means that you will loose your advantageous position on his 6. When you spot which side he breaks to, immediately pull LEAD - do not fly after him, fly to the future point where you will get to shoot him. It usually looks like a quick pull and unloading, taking a snap shot and extending thus utilizing your speed to get away for another pass / lag displacement roll, or any other option. This is what an "E" fighter would tend to choose.
Going for reposition means that once you spot his evasive, you forget about the shot attempt - COMPLETELY. Concentrate on flying the plane. You'd want to do some "out of plane" maneuver (and against what it sounds like to me, you do not actually go out of the plane. That is crazy), hi yo-yo, lag displacement roll, etc. and go for a lag pursuit - you are currently too fast and thus your turning circle is almost certainly larger than his, no matter if you are in a N1k and he is in a P-38. First outfly him, only them think about your guns. If you are the better turning plane you will wear him down quickly, but only when the speed get low enough so that non of you can pull into a black out will you start to feel the difference. Even then remember the key thing: Planes almost never fly on the same circle, so do not think in terms of "my turn rate vs. his turn rate" - it rarely work this way.