kinematics - Can there be motion without the flowing of time?

tldr - Can we reject the notion of the passage of time, but still accept that motion is real?

This question is a follow up to comments between myself and the author of this answer to the question, What is time, does it flow, and if so what defines its direction?.

The proposition is that time does not flow on the basis that:

No it does not. Water flows. You can see it flow. But when you try to see time flowing, all you can see is cogs turning or a crystal oscillating. The notion that time flows is just a figure of speech, an abstraction. Light moves, planets move, blood moves, electrochemical signals move, cogs move. Everything moves, and you can see this motion. But you can't see time flowing. Because it doesn't.

My counter argument is that the definition of motion involves the passage of time. From wikipedia:

In physics, motion is a change in position of an object with respect to time.

Therefore, if we want to reject the notion of the passage of time, we must also reject motion. If time does not flow, then it is like the spacial dimensions, and what our brains interpret as motion and time flow are really just fixed coordinates in spacetime.

Furthermore, that you can't see something doesn't prove that it does not exist. We cannot see an inverse square law, but we can deduce it from observation of things we can see. It is an abstract concept, but we accept it as reality (or at least until an alternative theory replaces it, but the issue here isn't whether or not today's science is correct).

The response argument runs as such:

When you define motion as a change in position of an object with respect to time, remember what a clock really does.

My issue with this is that it appears to involve circular reasoning:

1. Motion is a change in position with respect to time.

2. The passage of time is not real, because when we observe a clock we are really just observing its cogs.

3. The cogs are undergoing motion - go back to line 1.

So, who is right? Can we have motion, without the passage of time? If so, what is a more accurate definition of motion, which does not contain a circular reference to motion itself?