I was aware of the lack of spherical symmetry. However, it is intuitively obvious that in the 2D situation of a disk-like galaxy, embedded mass scales as the square of distance rather than the cube, as for a sphere - e.g. a globular cluster.

Gauss showed that both a hollow shell of mass and an annulus exert no gravity on a test mass internally

Therefore, a test mass would fall through this 2D system faster than through a 3D system, since the mass is more centrally concentrated (a complex mathematical point, but a simple spatial observation).

In summary, the galactic disk would act more like a point mass than a sphere and NEITHER case matches SM"s dumb-ass calculation.

(one solution is to find what point mass is required at the galactic centre for the Sun to orbit at it's distance and period, then do a gravitational acceleration integration from rest at the Sun's distance. This is the minimum time to fall, and other more complex models of Mass distribution may be adopted to derive the value for an assumed uniform sphere of mass (stars+dark matter))

Perhaps I should have simply worked the maths and showed that SM had, as so often, screwed up his calculations, but I have no time to rework the mistakes of an idiot savant.

Or perhaps I should have simply asserted that he was wrong.

David Mayer's reply is unhelpful. While my initial model may have been inappropriate for the case of a galaxy, it is not so wildly inappropriate as to invalidate my point that SM was wildly wrong in his calculation.

I was trying to offer some different ways of viewing the situation that might help him conceptualise how he messed up the maths.