Regarding big wheels:
Keep in mind also that adding drag below the CG is destabilizing in pitch. It produces the same effects as a thrustline located above the aircraft CG -- a tendency to pitch over. The magnitude of the pitchover tendency in this case increases as the square of airspeed, and is independent of throttle setting.
A gyro the size and weight of a Gyrobee doesn't need G.A. airplane wheels. A stock Gyrobee will leave the ground at about 18 mph. It is best to lower the nose and unstick at 25 mph instead, but even that speed does not require anything approaching the robustness of G.A. airplane wheels, bearings and brakes. Go-kart wheels with high-speed bearings are more than adequate. I use Azusalite nylon wheels on my Gyrobee.
On grass, brakes aren't very necessary, either. I use a plywood scrub brake on the nosewheel, exactly per Bensen, and it's more than adequate. If you insist on mainwheel brakes, then use the brakes marketed by the go-kart people for your go-kart wheels. On a Gyrobee, you will need to alter the attachment of the inner end of the main axle tubes, as the plans version is secured by a single bolt and does not resist rotation.
It's surprising at first to realize how much thought, trial and error have gone into optimizing designs as the Gyrobee and Bensen. They have a casual, thrown-together look that is very misleading.
After owning one of these craft for awhile, you develop a healthy tendency to give the designers the benefit of the doubt. When you start thinking about "improving" some component, be aware that the designer may well have gone down that same path, realized why it wouldn't work, and come up with the version you see right in front of you.