I run mostly dirt and occasional asphalt. Luckily I have another chassis I was setting up for asphalt and specifically run a 206 only on asphalt. Vega's are almost definitely the tire of choice, almost brand new out of the package they are fast, but I suggest scuffing them and let them sit a month. Firestones and Hoosiers are pretty good besides that, Maxxis are junk, Burris are junk, Unilli are junk. Never seen Kings around here, so can't say. This is specifically for asphalt!
The typical oval setup for us is
4.50 on a 6X6.50 wheel for the left front.
4.50 on a 6x6 wheel for the left rear.
Then 800's on 10's for the rights.
This should get your stagger the same as most dirt racers run, 1.50, and 1, and can adjust the rear per track. IF you absolutely know for sure you need more stagger, you can mount the LR on a 6.50 wheel and it will get your that 1.50 in the rear and can swell if you only need 1.25. Only difference is you will have to adjust your track width per the wheel you decide to run. A 600 will make the kart WAY too tight for asphalt if you ever get any grip, and you'll struggle and be quite slow.
If you prep, I wouldn't wipe much of anything on the outside, and use a VERY VERY non-aggressive prep inside. As far as kart setup, as snow mentioned above should get your close. The biggest thing will be adjusting rear tread width to match your new smaller LR.