Grand Funk Railroad’s I’m Your Captain (Closer to Home). Always felt the narrator has died and become a Flying Dutchman type, doomed to forever be at sea, always getting closer to home, but never making it.
Damn, I want to include Keep Me in Your Heart on The Wind, Warren Zevon’s last album, because it is brutal to listen to, but I am not sure if you can count the narrator as quite dead yet.
“The Highwayman” by The Highwaymen (Willie, Johnny, Waylon, and Kris) tells of the singer’s previous incarnations and deaths, and current life and expected death.
I wish I posted that.
Oh wait … I did
Not the narrator, but 30,000 Pounds of Bananas is a Harry Chapin song that is all about a truck driver who dies when he loses control of his truck during a steep descent into Scranton, Pennsylvania.
And nobody can take away your achievement of being the third person to mention it. 
New Order, Love Vigilantes
When I walked through the door
My wife she lay upon the floor
And with tears her eyes were sore
I did not know why
Then I looked into her hand
And then I saw the telegram
Said that I was a brave, brave man
But that I was dead
And how about “Constipated,” his Avril Lavigne parody?
Why’d I have to go and get myself decapitated?
This really is a major inconvenience, oh man, I really hate it
Such a drag, now can’t eat, I can’t breathe, I can’t snore
I can’t belch or yodel anymore
Can’t spit or blow my nose or even read Sports Illustrated
I cocked the pistol pulled the trigger and all I saw was red
I gently stroke her arm as she lies lifeless on her back
Then placed the barrel in my mouth, all I saw was black
Johnny Cash and Sting both came close:
*Early one morning
With time to kill
I see the gallows
Up on a hill
And out in the distance
A trick of the brain
I see a lone rider
Crossing the plain
And he’d come to fetch me
To see what they’d done
And we’ll ride together
To kingdom come
I prayed for God’s mercy
'Cause soon I’d be dead
I hung my head
I hung my head*
Also 1963.
From the folk music side:
Cindy Mangsen does an eerie song called Little River about a drowned sailor.
“Spring comes warm to little river,
Storm comes black,
I was heading home when the indian giver,
Took me back.”
Nothing in the song says the singer has actually died.
While the first verse is about constipation, the name of the song is A Complicated Song, a parody of Complicated.
I always thought that Come Sail Away by Styx was such a song: The singer is sailing away, thinking about his life, seeing angels.
Bruce Springsteen’s “The Rising”, from the album of the same name, is narrated by a New York fireman climbing the World Trade Center stairs and arriving in heaven.