The long “Saint lists” appear mostly in the Eucharistic Prayer - considering what is happening and who is made present on the Altar, you’d have a recollected posture anyway.
For the priest’s part, it often works best as (for example): “…in communion with those whose memory we venerate, bow head especially the glorious ever-Virgin Mary, mother of our God and Lord, Jesus Christ, † and blessed Joseph, her spouse, de-incline head your blessed Apostles and Martyrs, Peter and Paul, Andrew, James, John…”.
During the EF, due to the silent canon, the laity wouldn’t hear the names said anyway - but, just like the OF, they would be in a reverent and respectful position due to what is happening at the Altar.
These sort of little gestures help us to acknowledge something special is happening and that it is real. To that extent, if they become important in and of themselves, separated from the Sacred Liturgy, they are a mockery of Divine Mysteries. Reverence the names if and when you hear them stand out - eg. a homily, the day’s collect, etc. While I’d be the first to argue that rubrics are there to be followed, do so with common sense and (I’m assuming you’re a pew-sitting layman) don’t let the mechanical function (crucial though it is) to overshadow your prayer, but let it be an extension of your active (interior) participation.