Well...while you're out there chillin'...just remember I have never called an American a 'merkin'....not once...and I have no idea what one might be.
I do call them 'Merrycans' in as much the same way as Aussies are often referred to as 'Arsees' as in 'arse' as there appears to be a pathological inability to pronounce 'Aussie' as in 'Oz' a-la 'The Wizard of Oz'.
Australians tend to be as lazy as they can get away with and will often abbreviate even simple words to something more ridiculous so 'Yanks' is just the one syllable way of saying the four syllable 'Ah mair ric kans'....and why we are 'Aussies' or 'strail-yans' because we're halving syllables yet again.
Most of what you find offensive is not that at all, and when an attempt to be 'US-friendly' with vocabulary you get your knickers in a twist yet again.
BTW....the rhyming slang for 'Yank' [probably stemming from embitterment during US shore-leave in WW2 in Australia [over paid, over sexed and over here]] is 'septic' as in 'septic tank' - 'Yank'....oh. and 'Yank' comes from around the same period 'I'm a Yankee Doodle Dandy'.
 
As for Texas and cattle Stations...the anecdote dates back many years....20 or 30, so it may get a bit hazy and that link may not be the correct target, anyway....
 
Anythin' else ya wanna know 'bout Are-sea lingo?....