, thanks for sharing! My experience is mostly with the Slavic tradition and I've never heard the Irmoi left out. Though, when we do a short moleben, we often don't sing a canon at all, but only the verses. The clergy will sing the refrain, "Most Holy Theotokos, save us!" (or the appropriate saint, e.g., "Holy Greatmartyr and Healer Panteleimon, pray to God for us!") and the choir repeats. The clergy then sing, "Glory..." and the choir responds, "Now and ever..." Then the clergy say again, "Most Holy Theotokos..." Each cycle in this is considered an "ode" and is broken up in the appropriate places (such as for the Gospel reading).
Also, for the record, we usually don't sing the katavasia at my parish. Ever. The only time I can think that we actually do sing them is during Holy Week, particularly the Canon of Holy Saturday, for obvious reasons. I look forward to learning more about the Greek practice about this and many other things.