Deep breathing vs. buoyancy question

Pretty new diver here, about 40 dives, and looking for advice.

Just finished up a week of dives in Grenada, and made a point of paying attention to air consumption. Based on Internet advice, I focused on breathing deeply and exhaling completely, counting 4 seconds in, 6 seconds out. Doing this, my computer reported average SAC has dropped from about 0.8 to 0.5, and I'm not the one calling dives for gas anymore. This seems like a great improvement.

However, my buoyancy goes to shit when I'm doing this. Breathing more "normally", I can maintain a neutral depth with good trim. But with this more efficient breath control, I go up and down several feet with every breath. This actually makes it pretty easy to control when I ascend and descend, but obviously isn't great for most of the dive.

If I try to breathe normally-but-slow, I feel like I'm hyperventilating.

So what's the trick here? How do you both breathe efficiently and control your buoyancy?

I think I'm pretty well weighted, since I have no problem maintaining my safety stop with the shallower breaths.