GUEST, GUEST -
There is no issue of tempo (faster or slower) or of changing tempo here. 6/8 and 9/8 are different meters, not tempos/speeds.

6/8 is a duple meter (2 beats) and 9/8 is triple (3 beats).

Do I imagine it as feeling possibly awkward-feeling to step/walk, around a capstan to a meter of 3 beats (9/8)? Yes, I do, because I have 2 legs. This appears to be why, though cultural outsiders tend to "hear" the Ewe agbekor rhythm as a 3-beat meter, Ewe people actually parse it in 2 beats to align with their 2-legged dance.
Nevertheless, examples of people marching to 3-beat tunes exist, though I suppose they are fairly rare. One example I can think of is "Green Hills of Tyrol," which I used to play on bagpipe, and which Highland regiments seem to get on just fine in marching to. So, my subjective *feeling*, projected, doesn't amount to a persuasive argument to doubt that the reference is true, i.e. that "Drops of Brandy" was a fife tune used for marching around the capstan.

These are not chanties, as chanties are songs, sung (hence "CHANT"), so that part is fairly irrelevant. I can't think of any chanty in a 3-beat meter (e.g. 3/4 or 9/8). The chanties are in 2-beats or (the kinesthetically equivalent) 4-beats (e.g. 2/4, 4/4, 6/8). The genre was based in actions that are duple in their nature, meaning that 2-beat meters gel correctly with the actions, 3-beats does not. The formal parameters of chanties, I believe, were regulated (and thus established) by their chief applications and the kinesthetics of those applications, which were duple-metered actions upon halyards and brake windlass. The whole chanty thing, in any case, is a different phenomenon whose aspects don't necessarily apply here. Different cultural histories, different time periods, different work.

This is about instrumental tunes that were employed in the period before chanties, during the kinesthetically different application of a huge capstan complete with messenger cable, nippers, and a large crew. The whole "nipping" process made such work painstaking.

Before the mid-19th century, Anglo ships' crews were enlivened by fife and fiddle tunes, we know. These references provide a credible record of what some of those tunes were.