OK, I've done some more research. I've got a few mistakes in my comments above, caused by the fact that the ATV is 30 miles and one day away from my computer. Here are the details as I now understand them:

1) The service manual has an exploded diagram of the carb. It shows the front (pilot air) screw to have a slotted head.

2) The service manual also has a closeup view of the pilot air screw in its discussion of carb tuning. This too shows a slotted head.

3) The above two views are line drawings, not photographs. They are consistent with each other.

4) The two respondents on this thread say that their machines have Phillips heads on their front (pilot air) screws.

5) My machine runs much better with the Phillips head screw in the front position. This agrees with the two respondents but disagrees with the exploded view, the enlarged view of the pilot air screw, and the online parts references of both World of Powersports and Bike Bandit.

5) The manual also has a few actual photographs of the carb. None are clear and the contrast sucks, but I've been spending a LOT of time with the manual lately trying to figure this out and I finally noticed that in two of the photos the screws are just barely discernable. Guess what? The photos show the Phillips head in the FRONT position - in agreement with our three actual machines, but in disagreement with all other documentation I've been able to find including Suzuki's own manuals.

My conclusion: The Phillips head screw is indeed the pilot air screw. Somehow, ALL of Suzuki's drawings (i.e. non-photographs) have it backwards. The photos are correct, the drawings are wrong. Amazing, but at least I think I got to the bottom of it.

My last remaining problems are these:

1) When I hold the throttle at about 50% (that's where we have it limited with the screw on the handlebars), the engine revs right up, holds its speed for a moment, and then the RPM's ramp way up again to a new high. They stay there until I release the throttle.

2) If I hold the throttle at that 50% for a while and then suddenly release it, the engine will slow down to idle RPM's and then sometimes just die. It restarts immediately with a pull of the cord.

The only thing I've actually adjusted on this carb is the float height. It was about half of what the manual specifies. Thinking about it, that means the float was leaving the needle valve open longer and allowing more fuel to accumulate in the float bowl. Now that I've adjusted it "properly" according to the manual (0.96-0.98 inches), I wonder if at high throttle the engine is starving for fuel... which could cause it to run lean and thus bump up its RPM's. When I release the throttle, there's insufficient fuel to keep it running at idle via the pilot jet alone and so it dies. Perhaps someone intentionally lowered the float to compensate. There's nothing in the manual that suggests such a float adjustment is appropriate, but then we've just learned that the manual isn't the most reliable source of information.

Anyone care to speculate on my "bump in RPM" and "dies when throttle released" problems?