I ran into a similar problem about 6 years back when I did a quick restoration (static only) on a 6 pdr gun from a local surplus store. I ended up welding the outer portion of a set of jeep rims onto the 6 pdr rims, and then using the origional 7-16 jeep tires. They cleared the shields, so anything smaller should work out allright.
The few times I towed it around, it really could start to bounce on pavement over 30mph.
If you ever pay a visit to Trenton air base, and look at some of the tires on the ground support equipment, such as the APUs. Those industrial tires are fairly heavy duty and come in sizes and tread patterns similar to what you are looking for.
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