OK, it's getting clearer. Your circular path around the Sun is a large scale Sagnac effect experiment?

We know from laboratory experiments that the Sagnac effect occurs there.

From what I've just learnt about two-way time transfer, the signal travels over the same path in both directions, so this should not show any Sagnac effect, which requires the paths to form a loop enclosing an area.

Is there a two-way time transfer system that should show the Sagnac effect but doesn't?

You could make this much easier for both me and the journal editors by simply deriving a theoretical prediction of the result of an existing experiment and showing that the actual result is not what you predicted.