Liturgical Question

Good fellows, this question has been bugging me for years - now that I have a good number of Latin Traddies reading this blog, I thought I might ask you chaps:

When the Divine Office is sung by laymen, what (if anything) does one do about the Versicle 'Dominus vobiscum' and the Response 'Et cum spiritu tuo'? I've heard from one source (who is not to be regarded as authoritative) that it is replaced with 'Domine exaudi orationem meam' and 'Et clamor meus ad the veniat', but that leaves a rather awkward order when 'Dominus vobiscum' and 'Et cum spiritu tuo' are followed directly by 'Domine exaudi orationem meam' and 'Et clamor meus ad te veniat'. I haven't seen any instructions on this matter anywhere - does the presiding layman sing the Versicle?

While we're at it - what changes to the order and texts are made if the Office is sung by laymen (or a lone layman even)? I'm curious because the Byzantine Offices have clear provisions for what is to be omitted or replaced when a Reader presides, yet the Romans don't seem to have an equivalent set of instructions. My thoughts were that this is because the Byzantine Offices are often done by laymen without a priest, yet in the Roman uses, the Divine Office has become a highly clericalised thing that was no longer considered really the common property of the faithful, hence the proliferation of votive hours (of the Virgin, of the Holy Spirit, of the Holy Cross...) in the West.

Anyone out there able to answer this one?