At least in American English “next to best” would mean second whereas “next best thing” means something likely to be the best thing in the near future and it’s a very common idiom.
"Next big thing" means upcoming good thing.
They want something that isn't likely to be misinterpreted, and I've never seen that phrase used to mean "next big thing", only "second best".
Big country though, could be a regional thing.
Note that "next bigGEST thing" also means the 2nd biggest thing.
But after reading the comments and thinking on it, I realize it's probably used more often in the context of 'second best.'
"Next big thing" is commonly used and unambiguously means what's intended here.
I get we're trying to go for "next [best thing]" but yeah I (also UK) read it as "[next best] thing" and can't think of any examples where I'd read it as the former