Quick and very fussy question I'm hoping someone with native-level Japanese could comment on.

My inclination (as a non-native learner) would be to translate 美味しくいただきました as "the staff enjoyed it later". It's both slightly more formal and elegant-sounding than the comparatively coarse "ate", and captures the pleasure implied by 美味しく ("deliciously"). I would expect plain old "ate" if they used 食べました.

Of course, I'm not a professional translator or native speaker! It’s possible I'm over-indexing on the textbook knowledge I have of the language and in practice, to native Japanese eyes and ears, the things I think I'm seeing aren't really there.

English doesn't have rules as clear cut as Japanese's for politeness—especially nuances! I think it's fine to translate it to "ate".

In turn, I'm not a native English speaker, but in the dictionary I searched in, "enjoy" isn't a synonym of "eat", whereas いただく definitely is—albeit a very polite one[1].

[1]: https://jisho.org/word/%E9%A0%82%E3%81%8F

English alternatives like “The staff enjoyed it later” or “The staff had the pleasure of eating it later” I would expect come across more euphemistic than normal to the average English-speaking viewer. So the question is whether the original was intentionally trying to come across euphemistic, or whether the original was using formal/polite language solely because of its position as being on TV.

IMO the bottom line is Japanese-English language pair don't translate natural AND verbatim at the same time. Either you're going to paraphrase heavily, e.g. "leftovers were shared with crews", "caution wet floor", or give it up and let it be "staff ate it", "here around is undergoing cleaning", etc. Some amounts of balancing act is always going to be needed.

What you say makes sense for explaining what was meant, but localizers might well simplify this kind of thing (just as they "punch up" other lines) on the basis of the significance of the line in cultural context. Basically, the 美味しく is culturally obligatory here (you'll see similar things in advertising copy), which causes it to lose meaning.

Not Japanese, but I feel if you translated it that way you would risk people reading the article into assuming the sentence could be used in ways that match the sense of "enjoy" in English that could never match the sense of the word used in Japanese, e.g. the staff enjoyed a movie later.

You're not wrong - "the staff ate it later" is a word-for-word translation, so it's kind of weird to leave out 美味しく. (among other things a meaningful translation would say "crew" instead of staff)

But the nuance of the JP here is that it's using a polite set phrase, not describing whether people enjoyed the food or not. A bit like how "a good time was had by all" is used to wrap up a story, not really to describe what kind of time people had.

tl;dr, 美味しく is there because the JP would sound weirdly flat without it, and you're right that "enjoyed" would probably be a better.