Nice ! How smaller in overall diameter is that spare ?
A quick search netted me those two.
Coker Tire 55592 - Coker Firestone F560 Tires - Overview - SummitRacing.com
Coker Tire 61975 - Coker Excelsior Tires - Overview - SummitRacing.com
May not be tall enough, barely 24 inches, but it's narrow ! And DOT-approved (although the second one requires tubes, grrr...).