Much of what determines whether a car pushes or is loose in a corner depends on the ratio of roll stiffness, front to rear. Roll stiffness depends on both spring rates and the presence of a sway bar. The air bags usually have a much lower spring rate than the original steel springs. So, when you put an air bag on each and every corner, the effect of the front sway bar is accentuated and the car has a lot of push. That's why they want you to remove the front sway bar. Unfortunately, while this minimizes the push, it means you're going to have a lot of body roll while cornering. Actually, their suggestion can be self-defeating, as the increased roll might mean excessive camber change at the front and you end up with a lot of push, anyway. So, your hunch is correct. If you want the car to corner without excessive roll, you still need the front sway bar and a husky one at the rear, too.
But, wait a minute! You said you want a "cushy" ride along with the good handling. Sorry, you can't get there from here, unless you want to spend some really big bucks (and I mean REALLY big bucks) for an active suspension. . If you want to be competitive in SCCA slalom, you're going to have a ride that will shake the fillings from your teeth. If you want a "cushy" ride, keep your speed well below the posted maximum for all highway curves.
As for myself, I prefer a car that corners flat and my insurance has good dental coverage, so I'd stick with the Stude springs. But, to each his own.