BTW, this is a (rare?) case where the speed limit for cars should be much less than bikes. The road is only a little wider than the park vehicle, and there are pedestrians and cyclists moving in both directions most of the time, as well as coming in from side paths. A vehicle moving at more than 5mph could easily hit someone.
An alert cyclist on the other hand could happily move between the pedestrians, even if they aren't sticking to their side of the path, at more than 10mph, unless it was very crowded.