I was judging from the announcers on Radio Moscow back in the day, zashibis, not from any information about language instruction specifically. So your information is no doubt better than mine.
And your second paragraph is of course spot on.
My general impression is that English learners make too much of the difference. I'm pretty sure OP won't sound either British or American when he speaks, but Georgian. You've got to get to quite a high level before the Atlantic divide becomes an issue.
