I too doubt the posh etymology: If you’re sailing around the cape by definition you will have crossed the equator twice, meaning your calculation of the sun positions will change. Acronyms pronounces as words seem more a modern 20th century thing.

Wiktionary talks about posh coming from the Romani language, meaning half, in monetary terms, as in half a crown. Seems believable to me, a lot of modern terms come from traveller’s languages and argots and such. See also tory and whig.