Truck Got Stuck. With a sung chorus to boot.
I came here to mention Richard Thompson but was handily beat to it, so naturally, my backup offering is “Peel Their Caps Back” by Ice-T.
Roland the Headless Thompson Gunner by Warren Zevon:
And another, ‘Veracruz’:
Surprised nobody mentioned this one yet:
Doesn’t quite meet the ‘spoken words’ part of the OP, but The Ballad of Pancho and Lefty has always been a personal favorite:
See this post 
. Nobody does Townes Van Zandt better than Townes.
Interesting! I did a search for “Pancho” and nothing came up. It must not look at the links.
This song will now always be lodged in my head as “The Ballad of @Beckdawrek and Her Wayward Kidneys.” (It’s a long story.)
Here are two from the solid gold year of 1970. Eric Burdon and War “Spill the Wine”
And Three Dog Night “Mama Told Me Not to Come”
Thanks @kenobi_65 , you’re such a loyal friend.
Dylan: Black Diamond Bay and Romance in Durango
The Band: The Night they Drove Old Dixie Down
Another great story song from “Desire”, besides your examples and the aforementioned “Hurricane”, is “Isis”. Maybe his second most cinematic song after “Lily, Rosemary And The Jack Of Hearts”. It’s an album full of story songs, and one of his best.
Three by the great Phil Harris:
That’s What I like About the South
[Smoke Smoke Smoke That Cigarette](https://www.youtube.com/results?search_query=phil+harris+smoke+that+cigarette
How about Steve Martin and Edie Brickell? Pretty Little One. (He says it’s a story song right there in the intro.)
I’ll bet the Hooker version kicks ass.
Spoken word with musical background, but no chorus.
I missed the spoken word requirement in the OP. Some of these have verses that are spoken/sung but I think they qualify.
You Better Get it While you Can - Steve Goodman
Vegematic - Steve Goodman
Beer Run - Todd Snider
Surprisingly, this hasn’t been mentioned yet (I don’t think):
Keeping on topic with the OP’s “spoken word” requirement:
“Spanish Train” by Chris de Burgh.