Yes, 'frolic' (froli
cked, froli
cking) isn't quite it, even though it's obviously cognate.
But of the rest --
rejoice, be jubilant, shout with joy, exult, any of those work for me. In its metrical translation, Bärenreiter has 'Shout ye exultant,' which is pretty good at least in matching the vowel sounds, if stiffer and less idiomatic. (And the next line, 'this day of salvation' is not good, because it introduces an extraneous concept.)
In the Christmas Oratorio (as opposed to CJ's text here from two years ago), the exhortation seems directed at the choir and congregation alike; it's not actually sung either by or for angels, but by and for Christians, in response to the biblical narrative, as with most Bach choruses and chorales. And while I'm not generally fond of 'ye' and so on in modern church texts, old-fashioned or literary words don't seem all that out of place here, as it's an 18th-century work.
For 'frohlocken' in particular I might be inclined to translate
be merry, which is often paired with 'rejoice' in English Christmas texts.
'Jauchzen' may indeed be rather loud, but it seems to cover a wide range of sounds. According to one of my bilingual dictionaries, other possible translations for it in more recent German include 'to cheer,' as in what an audience does, or 'to gurgle,' as in what a happy baby does.
Maybe German speakers could comment on other possible contexts for 'jauchzen,' or indeed, whether it's still used much at all, if that's what you're curious about.
OT: My all-time favorite text to that movement is the parody one quoted here:
related discussion: Weihnachtsoratorium (von Bach) - #7