I feel I have to put in a kind word for 'gotten'. I've a fondness for simple, straightforward, gutteral, chunky words. I like prose with some weight and heft to it. And I don't consider British usage superior to American usage.
Consider ...
It sounds like the Great Brain has gotten to you.
Finally, we'd gotten the last hatchery catalog and curled up on the couch to read it.
Baba had nearly gotten himself shot by a stoned, psalm-singing border guard.
There was no way he could get out of the mess he'd gotten himself into with the cholera flag.
That's clear, straightforward, robust writing.
I can't see any reason to work around 'gotten' in those sentences.
A quick search through 20 bestselling books found 'gotten' in nearly half of them -- and not in dialog.
Marquez, Kingsolver, Hosseini, Ludlum . . . These are excellent stylists.
I don't want to say one shouldn't dislike the word if that's your taste. I just don't see any indication that 'gotten' is being avoided by careful writers in general.