Dear MMD, I had a similar dilemma when trying to find a tire for
a Seeburg F, which has the same drive setup as an E.  My solution was
to purchase a piece of 3/8 OD by 1/8 ID (vacuum hose?) from NAPA and
cut it to a length a bit longer than the circumference of the wheel.
Then I cut a 2-inch piece of 10 gage insulated house wire (from 10-2
Romex, about 0.15 inch OD) and used it to connect the ends of the
hose.

When mounted on the wheel, initially the tire would loop up before the
contact point with the driven disc.  The hose was then trimmed a bit at
a time until it fit with a small amount of stretch.  The wire connector
was then secured with super glue and bent slightly to match the
curvature of the wheel.

The tire has been running smoothly and trouble free for four years --
easily 100-plus hours of use -- and it shows little sign of wear.

Regards, Larry Emmons