The fourth wheel is so it could run as a Lakester instead of a motorcycle at Bonneville, similar to the
Poteet and Main Speed Demon that runs two in tandem in the front.
Here's an earlier iteration that has a bubble top:
It's really quite narrow—the same width, height and length as a P-38 drop tank, just with a lower 'equator'.
Why not go to a 19" wheel? They were used on Ford and Chrysler in the 30s and MG in the 50s (w/ knock-off hubs). I think it was 28-31 Fords that had 4x19". You could fit BMW i3 tires that would be very appropriate for the vehicles weight, and they're 155-55/19 at 26" tall.
Coker sells Rolls Royce tires that are much larger if you want to run big 'n littles.