So sounds like I'm pretty much boned in the P-51. Guess I'm flying the 109 near coasts.
Careful for us Marines who fly 'em out of the land bases.

In the 109, do I want to be more aggressive, and actively make him bleed e to avoid my attacks, or do I want it to be more passive, putting myself in a position where I force him to maneuver, or risk giving up a shot?
A lot depends on the situation you're in. However in general, if you're engaging from a position of advantage, you want to be aggressive and force him to constantly evade to strip him of E and force him down. Never extend more than about 2000 yards, and keep as much of that separation in the vertical, rather than horizontal, as you can (that's one of the biggest mistakes I see; guys blowing through at high speeds and running out to 4000-6000 yards before reversing for another pass). This goes for ANY aircraft. The guys who stay within about 2k yards and very close to right above me are the hardest to deal with. This is especially important against the Corsairs, which can all pick up speed quickly in a dive (and maintain control authority up to very high speeds. Plus the rate of roll only IMPROVES with speed, while if my memory is serving me correct from FSO experience, the 109s all tend to suffer poor aileron and elevator response as the speed builds) so that makes it key not to give them room, or else they can go shallow nose-down and run away on you, then zoom back up to a position where you may now find yourself at a disadvantage.
If he's got the advantage, you don't want to maneuver too aggressively or else YOU'LL be the one getting bled dry. The goal is to entice him into over-committing to an attack, and force him to burn off energy pulling out of it.
If you're Co-E/Co-Alt, against the 1-series, as noted in earlier posts you want to start taking the fight up. However make damn sure you're Co-E or better, because the Corsairs all have a good zoom climb, and as I think was noted previously can be very deceptive of their E-state.
As for left vs. right turns, in my experience the only real difference in the handling at low speeds is that the Corsair is a bit twitchier to keep stable in a turn to the right than she is to the left, but I've never noticed an appreciable difference in either turn rate or radius so you're not going to gain much of an advantage in that regard. Rate of roll at low speeds IS superior going to the left, however it's not nearly as badly impacted by torque going to the right as it is in the 109s (which IIRC need some pretty healthy inside rudder to counter). And speaking of rudder, beware that big barn door on the Corsair's back end. You might THINK you're out of his guns, only to end up eating .50cal (I've caught more than a few guys by surprise that way. One of my favorites was a Jug a couple years ago who tried to pass me about 50 yards off my port side in a nose-to-nose co-alt merge. Kicked the left rudder hard over and nailed him as he went by

).