>Wikipedia and others claim that most ships transiting the
>canal use their own power for forward motion, and the mules
>are used only to keep them centered in the locks.

Correct. The the link I provided confirms that in the very first sentence on the page. Forward motion only, but not enough to provide the ship's rudder with steerage way, so the ship can't actually steer itself until the pilot calls for sufficient power to do so as the boat exits a lock into the next channel.

A pilot boards each vessel - no skipper is allowed to pilot his own vessel through the Canal - because the pilot is employed by the Canal and has specialized knowledge of each and every lock, each and every approach channel, and the unique details of each and every flight of locks. No skipper can be trusted to pilot his own vessel through the Canal. Besides that, the insurance underwiters would howl.

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