Re: As was common back then ...
You may be right, Jake.
It's worth noting that Sir Francis Drake's admiral, Francis Fletcher, jotted into his log of Drake's voyage on the Golden Hind on 20 August, 1577, as he sailed through the Magellan Strait:
"In these Islands we found great reliefe and plenty of good victualls, for infinite were the number of fowle, which the Welsh men named Pengwin … [The birds] breed and lodge at land, and in the day tyme goe downe to the sea to feed, being soe fatt that they can but goe, and their skins cannot be taken from their bodyes without tearing off the flesh, because of their exceeding fatnes."
On the other hand, as you've remarked, the penguin may have derived its name (or vice versa) from the now extinct great auk, last sighted in 1852, also called "penguin" by early northern explorers. The auk's scientific name, as you point out, is Pinguinus impennis (aka fatty no-flight-feathers).
That said, the great auk was given its name by Carl Linnaeus himself in 1758... centuries after Fletcher wrote his notes. So on the matter of whether both groups of species – auks and penguins (the latter of which stretch across six separate genera, never mind the species) – were named for the Latin word for fatso or Welsh for whitehead, IMHO the real question is which came first... Was Linnaeus being playful about the Welsh name when he sought to give a term for the great auk – that same great auk that was already called pengwin by other, contemporaneous sailors (at least according to Dutch explorer Willem/Guillame Lodewycksz in 1598, writing in Premier livre de l'histoire de le navigation aux Indes Orientales, par les Hollandois) – or were the sailors quoted in the Golden Hind using plain old Latin and/or Early Modern English/Welsh slang derived from the Romance and Latinate sources that are spattered throughout the English and Welsh languages?
Whichever way it went, people were calling the bird by that name before it was given its scientific classification.
If you're right of course, the better pronunciation is ping-gwin. Either way, it's interesting stuff.