I theorized that the brushed DC motors from the scooters might be biased to run better in a particular direction.  This appears to be true.

I hooked them both up to a supply and compared the audible tone they produced in both directions.  They both ran a little faster in the forward direction.

Craigslist had provided me with one E150, and one E100 scooter.  They look identical in size/shape/specifications, but the E150 motor does run a bit faster in the forward direction.

However, I discovered that both motors run at the same speed when I run the E150 in reverse, and the E100 forward.

Given I will need to mount one of them running backwards, that is a happy accident I can live with.

Now I don't need to go messing with taking them apart to tweak the brush advance.