I often found also the version πύξ λάξ δοντάξ, which seems a modernization. I also thought to have found the version πύξ λάξ ὀδὰξ, but later wasn't able to find anything else than entries regarding the common word formation of this terms, this could be a likely way the last term was introduced if it is spurious.
πύξ λάξ seems to be a common frase in modern greek (even if we leave out the band, the two terms aren't used outside of this frase). The two terms are unsurprisingly often used together in ancient greek, but I wasn't able to track their use in the context of Eleusinian mysteries. The frase often appears in lists of frases that consist mainly of the Delphic Maxims, with some additions.
This site had a version with "Ω ΔΑΞ" (probably a mispelling). I link it mostly because it's the oldest dated example I found online and because my german is bad enough and I might have missed some hints.
In an arguably funny way the fist edit to introduce the frase in the german wikipedia article was commented πρῶτον ψεῦδος (it is just the name of the preceding section). Not a real answer, but I hope it could help.