It's not about a "timezone", the article is about high precision time keeping and how to set a standard for it on the moon.

Because (according to the article) an earth clock when moved to the moon wold be a few micro seconds per day slower then it was on earth, causing drift.

So just setting UTC or UTC+1 isn't the ting they're trying to decide. It's more about a scientific method to derive highly accurate time on the moon, which can't just be earth type atomic clocks because they would drift.

Wouldn't the solution be to use microseconds? Maybe I'm just being naive, I love science, but as I get older it gets hard to keep all the whims of tech in my head.

tech/science*

Yes, that would be the solution.

Do you know how to make a microsecond on the moon? No, you do not. No one does. NASA has been assigned to figure it out.

A clock that ticks in microseconds on Earth will tick in (local) microseconds on the Moon.

No, no. Time is a function of the gravitational field. Two different masses, two different ticking and tacking.

The consensus is that gravitational time dilation occurs has a constant effect, not that it's qualitatively different in some complicated way that requires a Presidential directive to figure out.

Do you have any evidence that they're more "different" than Earth "local microseconds" versus moon "local microseconds"?

A microsecond up there is different from a microsecond down here, because of gravity difference, kinda like interstellar but much much more subtle.