It's sound's like you've got it. Big picture is your "slalom ski turns" will take you in a direction that is angled downwind.
On the lake/flats, allow yourself to drift a fair amount downwind as you make your turns. It may be as much as 45 degrees off the wind. Then, you'll tack back upwind. So if you make 20 perfect slalom turns, you'll have to earn the distance lost by gaining it back with upwind edging.
Tighter slalom turns are trickier than lazy slalom turns. Use your ski edges softly. Maybe like you are skiing a green run at the resort. Like you pointed out, its more of a rhythm/timing thing. The harder you turn, the more likely you'll stall the kite or the kite will lose tension and collapse. The stall/collapse effect going to happen and is part of sussing it out and finding the right rhythm and ski edge pressure. The earlier posters explain this technically better than I can. I just don't know anything about waves or water so I chimed in
On the flats you get a downwind run of turns and then pay your dues with upwind tacks to get back. On a hill, the mechanical forces create a different dynamic. If you've been watching other kiters and wondered how it works and can't replicate it on the flats, then you're right; it's different. You can depower your kite and then make turns directly into the wind. If wind and gravity align, the uptrack will be straight up the fall line and the slalom turns will be down the fall line. Absolutely the holy grail, and probably really what you wanted to hear!
(Steering the kite. For me on the flats making turns, I park the kite and don't really pump it or need to move it around. The fun is just skiing and enjoying the turns. I'd say equilibrium between ski edges and kite line pressure is the central dynamic. Power/depower isn't fundamental. It's easy to make turns on a fixed bridle kite. Yet your ski edging will actually redirect the kite, so the bar isn't the only thing that causes a change in kite direction or kite power. )