No, you would have to calibrate the clocks to run slower to match earth seconds when they are in the moon's weaker gravity. Or constantly sync them to an Earth time source with over two seconds latency.
NTP has several methods for dealing with large latency that could possibly be adapted.
Latency is different from a constant frequency offset.
Yup, or you could... not do that. Which would be a lot simpler.
But, using your own frame of reference, you now need to convert to and fro on each cross-access. I don't really see the advantage. Notably, there is no such thing as an ontological second, it's an abstract measurement unit (loosely) bound to the rotation and revolution of the Earth. Moreover, there is no provision for such a cross-reference of basic progression of time in any Date/Time system currently available. Wouldn't be adding a constant coefficient easier? (Notably, we have modified basic constants several times, already.)