Good news — this is implemented.
It landed as a bulk action rather than a per-card button: select one or more cards in the verse list (long-press to enter selection mode), then choose Copy to 'New' from the three-dot menu. It works in any box.
What comes across to the copy: reference, passage, topic, image, note, link and labels. What doesn't: review progress, level and schedule — every copy starts fresh in your New box, so the original's hard-won progress isn't diluted. If you didn't mean to, Undo is right there.
One thing to flag, since it's a step short of your exact use case: the copy inherits the original's Bible version, so you still open the new card once and switch the source to your second translation. What it saves you is re-typing the reference, re-picking the image and re-entering the topic — the tedious part. Selecting several cards at once and copying them in one go makes that noticeably quicker than adding each verse a second time by hand.
Thanks for the suggestion — it's in the 6.8.10 line.