As a philosopher, I was hoping for a philosophically deeper definition of time.

This is why you should write about it. I am only here for the physics part :)

The concept of time is controversial in my discipline (and sometimes even in yours).

Well. time is uniquely defined. Or at least the second is. But as soon as one starts to live in the world of the elementary particles, time is not special anymore and behave as any other spatial dimension. So here, I would not say anything is controversial bu instead well defined.

If less leaps means better clock, what about a tick-tock that makes people leap in clubs all the time?

Argh... :D