Last season, we used 2 of the pneumatic Skyway wheels on one end, then a pair of the poly wheels on the other (8.75 or so inch diameter). Since the poly wheels were not the
exact diameter of the rubber wheels, we "turned them down" by holding them between our knees and using a belt sander and a bit of elbow grease (not to mention finesse) to get them even and slightly radiused in the axial direction. Talk about a mess of black dust! Glad we did it at my employer's shop and not at school
Because we were climbing a steel mesh that year, we re-grooved the original channels across the tire using a 1/4 inch rat-tail wood file. The result was a bot that could climb the wire ramp (with a 110 lb. person on board) but still manage to turn, since the poly wheels were just a bit more slippery than the rubber ones. The axial grooves bit into the mesh on the way up to provide traction. This year the best way depends on your method of attacking the platform and whether or not you see it as a pushing/pulling contest.
As to turning and handling, you either play around with the geometry, center of gravity and traction, or gear it down to be a real brute to get the desired results. Adjusting for handling can be both a science and an art. At this point in the build, I think it depends on how much time you have left. Quickly try it on a different surface to see if things change dramatically. You might discover something.