  We study the correlation of orbital poles of the 11 classical satellite
galaxies of the Milky Way, comparing results from previous proper motions with
the independent data by Gaia DR2. Previous results on the degree of correlation
and its significance are confirmed by the new data. A majority of the
satellites co-orbit along the Vast Polar Structure, the plane (or disk) of
satellite galaxies defined by their positions. The orbital planes of eight
satellites align to $<20^\circ$ with a common direction, seven even orbit in
the same sense. Most also share similar specific angular momenta, though their
wide distribution on the sky does not support a recent group infall or
satellites-of-satellites origin. The orbital pole concentration has
continuously increased as more precise proper motions were measured, as
expected if the underlying distribution shows true correlation that is washed
out by observational uncertainties. The orbital poles of the up to seven most
correlated satellites are in fact almost as concentrated as expected for the
best-possible orbital alignment achievable given the satellite positions.
Combining the best-available proper motions substantially increases the tension
with $\Lambda$CDM cosmological expectations: <0.1 per cent of simulated
satellite systems in IllustrisTNG contain seven orbital poles as closely
aligned as observed. Simulated systems that simultaneously reproduce the
concentration of orbital poles and the flattening of the satellite distribution
have a frequency of <0.1 per cent for any number of k > 3 combined orbital
poles, indicating that these results are not affected by a look-elsewhere
effect. This compounds the Planes of Satellite Galaxies Problem.
