Across the Anglosphere people seem to use “generally” and “genuinely” almost interchangeably these days.
It’s “a couple of minutes” not “a couple minutes”. Americans tend to drop it for speed, but it kind of fits with the accent I guess.
As far as Americanisms go, this is my least favourite… They seem to be dropping the “go” from the aforementioned and it throws me right off the sentence every time.
Seems you’re putting too much thought into this. If you really can’t come up with one just try a random noun genetrator a few times until you find one you like.