NavList:

George you wrote:

"Second, there's a small "phase correction", because the surface of a planet
is only partly-lit by the Sun. It appears to the eye to be at its "centre
of brightness", which is slightly displaced from the geometrical centre.
The almanac allows for this; a computer prediction of the planet may or may
not have done so."

 

The phase correction may not be appropriate for lunars in any case. With a decent telescope on a sextant, the planet's disk is visible and the usual instruction is to place the center of the disk on the Moon's limb, bisecting it. Also, in the historical almanacs, there was no phase correction in the lunar distance tables. They were strictly center-to-center distances.

 

And:

"Nowadays, computation being so easy, any star near the ecliptic can be
chosen, but make sure that it has been correctly identified and named!"

 

And interestingly, it doesn't even have to be that close to the ecliptic as long as the star is far from the Moon. For a specific, a star with an ecliptic latitude of 45 degrees (a long way from the ecliptic) would be 45 degrees out of line with the Moon's direction of Moon if the star is 90 degrees from the Moon. At that orientation, the rate of change in the distance would be 0.707 of the maximal rate. A 29% reduction is acceptable for lunars (getting GMT to +/-15 seconds is not substantially worse than getting it to +/-12 seconds).