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Dave P:

You're probably better off keeping your glasses off regardless, so long as you can still get a crisp focus through the telescope.  Fewer lenses between your eye and the star means fewer opportunities for distortion.

"Averaging the times of the observations and the distances measured" is basically the same concept as advancing or retarding a line of position.  If the lunar distance is, say, opening at a rate of 0.5' per 1 min, to compare observations taken 1 min apart you'd first either add 0.5' to the first measurement or subtract 0.5' from the second.  Then you're "comparing apples to apples."  The results should be the same as clearing each lunar distance individually to compare to your trustworthy timepiece, but it's much less labor to average the sights first if you're reducing distances by tables.