If you don't get the check (I assume that you have the promise in writing - if you don't, they can claim that they never made it), and considering that they've stolen almost $1,000 from you, so it's not something you'd want to write off as a bad experience, call your local bar association and ask for references to attorneys who handle theft by a foreign manufacturer when an item of theirs is returned to them for repair.
Samsung has enough attachable property in the US that they aren't going to want to be on the wrong end of that suit. (Aside from owing you an S8, they'd owe you for your wife's distress, your distress, any actual monetary losses either of you suffered due to not having the phone available - and the most likely not inconsiderable legal fees. (It's that last one that would make them blink. Attorneys who work internationally aren't cheap. Samsung seems to have become a "customer service is word last" kind of company. But money is job one, and they won't want to lose any.)
I've found (and learned) over the decades that some donkeys just have to be hit over the head with a bigger hammer to get their attention.