One key that I know doesn't get stressed enough around my local area could, perhaps, be phrased "Take control."In your post you said "...my instructor's admonition against constantly adding/reducing air..." indicates he is talking about avoiding the yo-yo game. Yo-yo game-adding air, not waiting for it to overcome your downward momentum, adding more air, then floating up, dumping and repeating.
Any time you have new divers, you're going to see people occasionally starting to float up. (If the class is good, the issue will be knocked out in the pool.) There seems to always be at least one, however, that starts floating and immediately thinks, "I'm floating. I should dump some air." That's a perfectly logical analysis of the situation, but there's slightly more to it than that.
If you're floating up, and you just sit there and dump a little, then dump a little more, and so on, by the time you've dumped enough to be neutral, you're a bit (maybe more than a bit) shallower than you were. If you built up a bit of upward momentum, you may even need to become a bit negative to arrest your ascent. Either way, what happens when you descend back to your original depth? Yep, the air in your BC compresses, reducing your buoyancy, and requiring you to add air. If you add just a bit too much, the yo-yo cycle starts right over again. (This is where you can easily get stuck in the loop, constantly adding or dumping.)
What should a diver do, then? As soon as you feel yourself floating up, the *first* thing you do is *take* control of yourself. Use those wonderful fins to stop yourself from floating shallower (you just tip over slightly and kick). You now have *taken* control of yourself, so at that point, you solve the problem by dumping a little air, and repeating as necessary, until you're neutral again.
As long as you *take* control and don't just "let diving happen" to you, you don't need to try to rush to dump enough air to arrest an ascent. You've already stopped the potential ascent by simply kicking to hold depth, so you have as much time as you need to ease yourself into comfortable neutrality. Since you're not floating shallower while you get neutral, you won't have to add air to account for compression as you get back to your original level -- you've basically never strayed much at all from that depth.
The more experience you get, the more of a feel you get for buoyancy. I never actually float up during a dive, as I can feel the changes in my breathing and dump air while still "in the window". Even with new student divers trying to learn buoyancy skills, however, as long as they learn to *first* take control and *then* solve the problem, the yo-yo problem pretty much goes away completely.