I've constructed this from the singing of both Hank Cramer and David Lovine; the version by Cramer is shorter and skips one verse Lovine includes, which I've shown in my transcription below. The Cramer version has an introductory chorus which the Lovine version skips, but otherwise the differences are notated. There's still a few spots which I'm not totally confident in, but I feel someone more familiar with either sailing or the Washington State region should be able to fill in those gaps.

I've emailed Mr. Cramer to help verify the lyrics and see if he knows who wrote the song; I've invited him to respond here, but if he responds via email I'll post it here as well.

Transcribed by ear from the videos above.

ALL AROUND CAPE FLATTERY

CHORUS
All around Cape Flattery, Tatoosh* shone bright
Up the Strait of Juan de Fuca on a full moon night
All around Cape Flattery, Tatoosh shone bright
Up the Strait of Juan de Fuca on a full moon night

Come all ye jolly mariners and listen to my tale
It's of the Lady Washington, a wooden ship of sail
Where we praise the ?sheep? for tallow and the ?stern bergs? for their tar
But if you wanna get out of old Aberdeen town, you cross the Westport bar

CHO.

Out of Grays Harbor, Washington we motored north all day
Wished we had a southerly so we could set some sail
Rolling in the trough, thinking this will never end
Watch and wait for the helmsman to take her round the bend

CHO.

Well, it's nice to have an engine when that leisure comes in sight
The drone can help you sleep through a sloppy, choppy night
But to wake with a wind and a belly full of sail
Makes a motorboat ride by comparison to pale

CHO.

Orders came to furl ????, oh, lads, and sail the Lady in
The Olympic Range like pumpkins lit the night sky with a grin
"Topsails, course, headsails, lads, make it so," said Brown
While off the stern of Washington the blood-red sun went down

CHO. ** [If you're following Lovine's singing, skip to the ** marking below]

Past Neah Bay we sailed her, all on a flooding tide
To port we saw the shining lights of old Victor-i-ay
Past the Elwha to Port Angeles we were bound that night
As we ran before the win beneath a full moon's light

CHO.

** And it's great to have your right-hand mates trim her sailing coil
Plowing, rising, hanging, falling, green seas o'er the rail
Shooting stars, all ?scupperbound?, shimmer as they fly
For the decks in the dark like the emeralds of the night

CHO.

Makah Bay slipped by that night as by her way did glide ***
Off our port fog twinkled bright, old Victor-i-ay
Past Elwha to Port Angeles we were bound that night
As we sailed towards the east on a full moon's light

CHO.

So, you sailor lads and lasses, come take this advice for free
Hold your log exact while your underway at sea
For as the days go slipping by, your recollections fade
Like the misty morning summer's day may vanish in haze

CHO.

###################################################################

* I assume that "Tatoosh" here refers to the former location of the Cape Flattery Light, which now resides at Neah Bay; it could alternatively be "Tatoosh on right" but that makes less sense to me - seafaring people would be more likely to use starboard or port
** While the verse after the jump in versions is partially repeated, I felt it easier to separate the songs here.
*** Some uncertainty with these lines