I finished up the wheel replacement today with a pair of Vex Omniwheels, which have little rollers on them to allow movement perpendicular to the way they’re mounted, thus resolving the previous shearing force problems.
Unfortunately, since my motor shafts are 6mm single-flat and the Vex wheels are designed for 0.125″ square, I had to drill the wheels out a bit to make it work. Lacking a drill press, I made do with a slightly smaller drill bit, a hand drill, and a rotary tool, adding in a few screws to adjust the fit and to lock the wheel against the single flat. Although there were some mistakes, I think it turned out rather well:
The larger wheels get over bumps more easily, and they make it faster, both to turn and to drive—the omniwheels are especially helpful while turning, as they allow me to treat the system as a two-wheel system at the back instead of a four-wheel system like it actually is.