Harry,
I thought that almost all of the LEZ guys were using what used to be called the "Lamb" size tire, alternatively identified as a 11.400x5 by Rutan and liisted as such in the ACS catalog?
Doesn't the "x5" indicate the rim diameter, so that a 500x4 would be a no-go on any 5 inch wheel?
Even the original VariEze used a 3.40x5 (3.4" wide x 5" rim diameter). The Spruce Catalog says that the 11.400x5 is intermediate between the 3.40 and a full size aircraft 5.00x5 tire (i.e., it's the "Lamb" size). Speeking out of school as a VariEze guy, the 5.00x5's look like monsters to me (ugly!).
I seem to recall that the first number is the tire width and that the 11.400 is in cm rather than inches (nice mixed units!), so 11.4 cm = ~4.5 inches wide.