According to the sidereal period of the Moon's orbit around the Earth of 27.32166 earth days of 86400 seconds we get an angular velocity of $\frac{2\pi}{27.32166×86400} = 2.6617×10^{-6}$. (NASA's factsheet has the Moon's sidereal period at 655.728 hrs.)
If we use the NASA factsheet figures for the Earth mass of $5.9724×10^{24}$ kg, the Moon mass of $7.346×10^{22}$ kg, the semimajor axis of 384,400,000 m, and using a figure for 'Big G' of $6.6743×10^{-11}$, then we get an angular velocity of $2.6654×10^{-6}$. Kepler's angular velocity implies that the combined mass of the Earth and the Moon are too high.
Assuming that the figures are all accurate to the last significant figure, as stated, then there are possible errors of 0.0015% in Big G, 0.0017% in the Earth mass, 0.014% in the Moon mass, and probably as small as 0.0003% in the semimajor axis, but the error in omega is 0.139%.
How to reconcile ... what have I missed ? Or is it something to do with a time-weighted average separation that is somewhat closer to 385,000,000 m ?