Andargor has a good point about the aberration type.
You lose the racial abilities of your old race, and gain the abilities of the new. Level adjustment and racial hit dice are both racial abilities and would go away.
But then, where do your XP go, that went into all those levels that you didn't get due to LA? I believe you would keep the same XP total, and have a hard conversation with your GM about what extra levels you could take to use those XP, without gaining any major new class abilities. Paragon levels in the new race, levels in the classes that you already have, or NPC class levels might be appropriate.
edit: It's easier if you reincarnate into a race with a higher Level Adjustment. You just have extra abilities to use over the long, long stretch before you gain enough XP to reach the next level as modified by Level Adjustment.