Well given that Benedictine Daily Prayer isn’t really liturgical (unapproved translations, etc.) I guess it’s already in the realm of “private devotions” so one could adapt it as one wishes.
However taking the monastic breviary of the abbey I’m associated with, which is an approved liturgy, given that I’m not bound in obedience to recite
all of it, but only as much as my life situation allows (which happens to be all of it, but that’s my own situation), then if I can’t respect the verity of the hour I can just omit it. If I have to do that, I at least try to read the Biblical and patristic/hagiographic readings at some other convenient time.
However I think one could just call it “Office of Readings with a different psalm schema” and get away with it; in fact the Monastic Breviary gives a hymn to sing when the Office is recited “the previous evening or during the day”

The Office of Readings has the structure of Vigils anyway with the difference that most monastic schemas are divided into two nocturnes: psalmody and Biblical reading, followed by psalmody and patristic or hagiographic reading.
Note that at least in our abbey, oblates can also pray the standard Liturgy of the Hours, which is what I do most of the time because of its greater flexibility (I do the Monastic when my days are more stable and predictable, which is what I had been doing for the past three weeks; however this week looks quite busy so it is the LOTH for now). But I still do the Office of Readings very early in the morning as “vigils” (around 5:30 am most days). It’s my favourite time of day for prayer and the OOR/Vigils is my favourite Office. Our oblate director in fact encourages the LOTH rather than the Monastic Breviary for oblates as it’s much more suited to secular life.