I've seen this liturgy done two ways, not counting the Syriac Orthodox version: I've seen primarily Greek bishops flanked by twelve priests serve it at a temporary altar in front of the iconostasis, versus populjm, and I've seen Russian priests serve it behind the iconostasis, ad orientem.
I am in favour of the latter option. I've read compelling arguments to the extent the former is a reconstruction of what ancient liturgies are like; I do know this liturgy never fell out of use, so I can't say whether or not it is an organic tradition.
My thought is that for ordinary parish use, what would work best would be to take the anaphora of this liturgy and serve it with the standard liturgy of the catechumens, ad orientem, with the usual antiphons, vestments and so on, so the experience of attending it would be essentially the same as attending the Holy Saturday liturgy with Let All Mortal Flesh Keep Silent instead of the usual cherubic hymn. In that manner, the rite is preserved, without the risks of confusion that would accomoany serving it otherwise.
I think, by the way, this is what the Russians normally do.