It would still be possible to answer the speed question, you just get different answers for different substances (and even phases of the same substance) at the same temperature.

Since something like water does have those additional ways to store energy, my guess is it would be slower at room temp than another liquid with less complex molecules that have about the same mass each. (If there is such a thing)

Also I expect different answers for each of mean, median, and mode speeds.

So if I were jiggling, I think I could come up with a speed. I’d figure out how far I'm moving, and how long it takes me to move. So I could measure from far left to far right of the jiggle (let’s say 18in.) and then how far to go from far left to far right and return to the original position. If that’s 2 seconds, then that’s 1½ feet per 2 seconds which can be converted to any other speed such as km/hr.