Researchers figure out how to keep clocks on the Earth, Moon in sync
> A single standardized Earth/Moon time would aid communications, enable lunar GPS.
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> eeh, if they ever land on the moon again ;-)
I'd say as a proposal it was borderline *insane*. Why complicate time keeping on Earth where almost everyone lives for the sake a handful of lunar astronauts. Working in the CoM frame will work but at an enormous price in the complexity of the equations of motion and book keeping.
Ephemeris or Terrestrial Dynamical Time is good enough. Anyone doing ultra precise observation will already know how to apply all the relevant corrections to their data.
The main ones being GRB's detection will be 1s different at the moon due to light travel time. Clocks on the moon will run a bit faster due to its much weaker gravity but just like the fix for GPS satellites you could adjust the divisor so that it appears to tick at SI 1s rate.
For the number of people affected that is by far the simplest way out.
TDT already does well enough for all practical purposes.