Changing gears doesn't change length of the drive shaft. Changing rear ends might as the ten bolt pinion could be shorter than the twelve bolt pinion, but I would try it first to see how well it fits.
Tires stickyness is determined by the wear number on the side. If the tire is guaranteed to last a hundred thousand miles (a number around 300) it will be as hard as iron and offer no traction (but they are great for burn out contests). The traction rating is a reflection of tread design, not how sticky the compound is. Slicks have a rotten traction rating because there is no tread to grip the road, but at a drag strip they are glued to the track with rubber cement. This is why they grip well there but not on the street.
Tire size has width (measured in milimeters) the aspect ratio which tells you the side wall thickness expressed as a ratio of width to the tire height and the wheel diameter Which has little to do with the size of the tire.
I say this because a 13 car tire and a 14 inch car tire are about the same size. The 14 inch and the 15 inch is the same size as are the 16, 17, 18, and 20 tires. By the time you get to 22 inch wheels the tire is a black rubber band stretched around the outside of the wheel and offers no ride quality at all. But it is still about the same size as the 13 inch wheel car tire. Wheel size (OD) basically determines how tall your side wall is, or expressed in terms of racing, how far the tread is from the metal wheel that holds the tread flat against the ground.
Now a 13 inch trailer tire is tiny by comparison to a car tire's height, and a 22 inch semi truck tire is very very tall. But basically unless it tells you differently on the tire carcass most car tires are 28 inches tall (or close to it).
Specialty tires like a Mickey Thompson Sportsman will not be 28 inches tall; it will tell you if it is 30 inches, 33 inches or 36 inches tall right on the sidewall. It will also tell you the tire's width and wheel size, (but not the aspect ratio). All racing tires work that way and will have on the sidewall "Not intended for highway use; for off road use only". This is because the tires are paper thin for use on a dry race track. They will have little to no tire tread and the tread that they have will not work on a wet road.
NASCAR uses special rain tires for a wet track (made by Goodyear and uses the same aqua-tread design as their street tire) but they won't hold on dry pavement; and have a thick tread area compared to a race tire with paper thin sidewalls that allow the tread to roll and move around if driven on the street (causing you to break away and skid suddenly when cornering).
Best street tire I have found is a Pirelli Trofeo R, and the second best is the Goodyear Eagle ZR Gatorback. They stick well and wear well considering I spent a lot of time going sideways or doing burn outs.