My younger brother died suddenly last week (the 4th). It took us until two days ago to get the church to confirm a service on the 26th. We had conflicts with travel and travel schedules though, so waiting three weeks was not distressing.
My father died on a Sunday in February of 2007. The next day my mom talked to the parish, and was told “either this Thursday, or you will have to wait a week to the next Thursday” because it was booked other days and would have run into Ash Wednesday.