Just to be clear, the faster/slower distinction that you make is related to what I referred to as applying/separating. It is a separate consideration from dexter/sinister, just as dignity/debility is.
On the dexter/sinister front, I had a look in Lilly, whose use of the terms is often less than clear, but in some places he does seem to say that an aspect
cast to the right (clockwise) is stronger. So the confusion seems to have begun by the time he was writing in the 17th century.
By way of contrast, here is Firmicus (VI 10,4-5, Holden's translation) on the Sun and Jupiter configured by square:
If Jupiter and the Sun are conjoined in square aspect, and Jupiter, possessing the superior part of a dexter square, aspects the Sun posited in a sinister square with a menacing aspect, that configuration denotes the insignia of dignity through either his own merit or that of his father, but it also bestows increases and promotions to good and great honors, and it always grants recommendations with good testimony, and many of them will experience the merit of dignity.
But if the Sun, made superior and possessing the dexter side, aspects Jupiter posited in the lower place with a square aspect, that configuration will make one decorated with a famous splendor of nobility, but it makes the father’s wealth to be proscribed with a miserable confiscation; and it stirs up dangerous disturbances by strong and evil enemies.
This is very similar to an anonymous Greek text on aspects, so Firmicus was following an older tradition here. The text doesn't mention whether the Sun is applying to Jupiter or separating from it, but simply assigns greater impact to the planet in the superior (dexter) position, whether it is the faster Sun or the slower Jupiter.