bozon, I suppose your problem starts with the enemy at your 12, into guns range and in a Co-E situation. That is, the enemy start turning, you follow the con in the turn but he start going down and turning with you at his six, ending in a diving spiral move.
If the enemy is "good", he will stop his spiral dive as soon as you stop following him. So, if you abort the pursue and try to recover alt to start pure boom&zoom moves against him, he will do exact the same move but in the opposite direction at the same time. That is, you two will end again in a Co-E situation, but you will be no more at his dead six and into guns range.
If you want the kill, there are no more enemies nearby and you have no problems loosing a lot of alt, my advice is to follow the enemy in the spiral diving, but exchanging angles for speed and energy. Follow the turning dive but easing both, diving and turning. The enemy will not ease any of them cause he is still being "pursued", probably he will even tight the turn trying to catch your six, no problem with that. Give him your six and then convert the fight into pure vertical, but this time you will have clear E advantage over the con.
If you want to get the kill as fast as possible and dont want to give up your angles advantage, try to dive behind him doing a wide open barrel roll nosedown and cutting gas.