I think you have it backwards. The shorter tires are going to lower your speed in gear.
Best way to think of it is in terms of revolutions:
engine revolutions * gear ratio * final drive ratio = axle revolutions
Distance traveled per gear at max RPM is therefor a factor of tire circumference as distance will equal axle revolutions * tire circumference
Edit: Okay jnaut has it right, just saw the raised RPM for new trap
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