Can someone shoot down these ideas for measuring the speed of light in one direction?

This isn't a reasonable request to submit.

The point that Veritasium is raising used to be a valid point, around the year 1900. In effect it ceased to be a valid point when relativistic physics was acknowledged as the way forward.

Let me make a comparison:
There was a time that there was a theory of heat, called the theory of 'Caloric'.

Caloric was thought of as a substance that diffuses from material to material, conferring the property of heat. Caloric theory looked very strong. The higher the temperaturature difference the faster the rate of diffusion of Caloric. When Caloric enters a material it spreads everywhere, and eventually material reaches an even temperature thoughout. the fit between theory and experiment was good. In order for the equations to be that good of a fit Caloric had to be a conserved quantity. That is, Caloric theory implies there must be a law of conservation of Caloric.

Over time Caloric theory became untenable. And eventually Caloric theory was obsoleted entirely by the kinetic theory of heat.

The kinetic theory of heat comes with the message: "Look: there was never any Caloric in the first place, it only looked as if Caloric existed."

Once it has become clear that the kinetic theory of heat is the way forward it would be absurd if someone would raise the issue: "Here is an amazing thing: no chemist has ever succeeded in isolating pure Caloric. Chemists have isolated all elements of the periodic table, yet: still no pure Caloric!"

And the response to that is: "What are you talking about? There is no need to assume the existence of Caloric in the first place!"

Here is how that is an analogy for the concept of the speed of light.

The shift from newtonian mechanics to relativistic mechanics was that in terms of relativistic mechanics the metric of spacetime is the Minkowski metric.

$$ (ds)^2 = (dt)^2 - ((dx)^2 + (dy)^2 + (dz)^2) $$

This quadratic expression has strong parallels with pythagoras's theorem

If we simplify down to one spatial dimension the expression is:

$$ (ds)^2 = (dt)^2 - (dx)^2 $$

Professor Andrew Hamilton has a website where the concepts are illustrated with animations. I recommend you step in where the concept of the centre of the lightcone is introduced.

The animation depicts the shifts of plane of simultaneity as the perspective moves from one viewpoint to another, and back again.

The lightcone animations (and subsequent animations) illustrate that the lightcone is an invariant of Minkowski spacetime.

What that means is the following: before the introduction of the concept of Minkowski spacetime it was still possible to reasonably expect that there would be an underlying structure, bafflingly inaccessible to observation, and that light propagates through that underlying structure with a particular velocity. If an apparatus designed to perform a one-way measurement of the speed of light has a velocity with respect to that underlying structure then multiple processes must be conspiring to hide that velocity-with-respect-to-the-underlying-structure.

If you move to the concept of Minkowski spacetime then all of those conspiring-to-hide suppositions are no longer needed. If spacetime itself is Minkowski spacetime then all processes occurring in that arena proceed according to the geometry of Minkowski spacetime.

With the above in place I can now turn to the issue that Veritasium is raising. Veritasium:: "Here is an amazing thing: no experiment has been achieved that measures the propagation of light through the underlying structure!"

(The point is, if there is an underlying structure, and your one-way-lightspeed measuring device has a velocity with respect to the underlying structure, you will find that the speed of light is not the same in all directions.)

And ever since the adoption of relativistic physices, which was around 1910, the reply to that has been: "What are you talking about? There is no need to assume the existence of an underlying structure in the first place!"

The point that Veritasium is raising in that video is outdated - by a 100 years.

(This doesn't necessarily mean that it is inherently impossible to perform a one-way measurement of the speed of light. The point is, even if you do perform such a measurement, the outcome won't be a surprise; it will tell you something that you already know: the speed of light.)

Later edit in response to comment by NDewolf:

There is simplification in that Veritasium video, but I wouldn't rate it as oversimplification. I get the impression from the video that Derek believes he has made a significant discovery. But the point he is raising has been raised before, and the way Derek treats it is clumsy. (Obvously Derek believes his treatment is sharp.)

The way this issue should be approached is to examine the question that the physics community was faced with after the introduction of the concept of Minkowski spacetime: "Should we continue to think in terms of he way that Lorentz accounted for the null results of the Michelson-Morley experiment and the Trouton-Noble experiment, or should we move to the concept of Minkowski spacetime?"

If you move to the concept of Minkowski spacetime the issue of one way speed of light becomes moot, the speed of light is an invariant.

I concur that the issue of Lorentz/Poincaré approach versus Minkowski spacetime is still an issue worth examining, if only to know exactly what it is you are choosing for.

About the video:
In terms of level of being wrong in an educational video: it's one thing to give the wrong answer. Worse than that is to ask the wrong question.

About the task of keeping clocks in sync:
Around the world there are multiple centers for time keeping, each operating multiple atomic clocks. These centers maintain a single worldwide coordinated time: UTC The procedures to maintain that synchronized time do not involve Einstein synchronization procedure, that wouldn't work. The engineers in charge of that work know what they are doing; they make sure that a single coordinated time is available, worldwide, to nanosecond precision. Example: astronomical observatories rely on that timekeeping for worldwide coordinatation of observations.