HiJack, turning nose to nose to gain advantage results in front quarter shots. That is NOT a head on. A HO'er is one that comes in on the initial merge, tries his damnedest to shoot you in the face, extends out 2000+ yards, reverses and tries it again. No attempt is made to gain angles, or to decrease angle off tail.
Now going back to the constant front quarter passes that occur in flat turns, there are a couple of things you can do. First, you can take your turn out of plane by going into the vertical. Sometimes by doing so, you can roll your lift vector onto where the bandit will end up if he continues his flat turn. This can provide you with the opportunity for a safe snapshot (compared to the dangerous front quarter passes you've talked about) or to gain the angles advantage and work for the rear quarter shot. Another thing you can do is to switch the turn, if it's advantageous to do so.
Almost all turns in Aces High 1 v 1's seem to be nose to nose turns (you turn left, bandit turns right and you form one circle, and basically get a flat scissors in a stalemate.) The advantage in this turn is first to the plane that turns tighter (smaller turn radius.) Also, a plane with a roll-rate advantage can do well in the nose to nose, as you have to reverse the turn after the pass to continue nose to nose (and almost every AH adversary does this.) So what you can do is switch the turn to nose-to-tail by continuing the turn and not reversing it as your opponent is still doing (if he doesn't reverse either, then it's still nose-to-nose.) In an initial nose-to-tail the plane with the faster turn rate, not turn radius, will gain the advantage. By switching to a nose-to-tail from a nose-to-nose you gain an initial advantage by not having to reverse your turn. You will also increase the lateral separation, giving you more space to take advantage of your decreased angle off tail.
The best thing to do is go into the more advantageous turn immediately after the intial merge. You need to know your enemy's capabilities and have a good judge of his speed/E-state. If you enjoy an E-advantage+climb advantage at the merge, going vertical is good. If he goes with you, you'll be able to get on top of him and dictate the fight. If he doesn't, he's meat on the table. If the E-advantage is his and you both go vertical, he'll probably get the angles. If he doesn't, you can possibly gain angles on his flat turn. If you both go for flat turns, going nose-nose is preferred if you are slower, yet turn tighter. If you turn faster, yet not as tight, go nose-tail.
The real trick is to be able to do all of this without thinking consciously about it. That's something I can't do.
I gotta think, and it gets me killed more often than not.
Of course, all this is moot when there are more of them than there are of you.