Well, I think your definitions are a bit of semantics. "Near imminent" = lurking, because the surgery is scheduled, therefore the danger of death is knowable and predictable. Imminent means "about to happen", like a dangerous surgery.
If a priest gave you exteme unction 2 weeks before a surgery, that's not correct. More than a day before? Kinda extreme, unless (in our day and age) that's the only priest available. A day before? Makes more sense. In other words, you might die tomorrow in surgery = near imminent.
Well, the other side of that coin is the priest could have given you EU a day before the surgery, but after surgery you never regained consciousness and died 2 weeks later = good thing you received EU when you did.
Or he gave you EU 2 weeks before the surgery but you died a week before surgery = good thing you received EU when you did.
Sometimes it might only make sense with hind site.