Mrs. Potter's Piano Pie

I've always thought that American Pie and Mrs. Potter's Lullaby are very similar songs, although I could never (and still can't) quite put my finger on why. Here are a few of my own thoughts on how they're similar: They're both fairly long; they're both a kind of pop/folk blend; they both have deliberately obscure but colorful and intriguing lyrics; they both have a narrative structure, but only loosely so; they both feature strong piano parts but are totally amenable to one guitar and a campfire situations; there's an intense desire to sing along even though no one ever remembers all the lyrics. Beyond these, I'm not sure how else to compare them. I suppose you could call them both ballads, but I think they're a little too unstructured narratively to fall into that category completely.

Anyway, tonight I heard Piano Man on the radio and it struck me as falling into a similar, if not the same, category. And this got me thinking, what other songs would fit?

So here are my questions: 1) If these songs are of a common and fairly unique category, what is it called or what should it be called? 2) What other songs, if any, fall into this category?

Here are a few I came up with after a quick scan of iTunes. None of them quite seem to fit, but they're close:

Furr, Blitzen Trapper
Stairway to Heaven, Led Zeppelin
The Weight, The Band
Feeling Good Again, Robert Earl Keen
Hey Jude, The Beatles
You Don't Have to Call Me Darlin', David Allen Coe
All These Things I've Done, The Killers
August and Everything After, Counting Crows
Nightswimming, REM
Hallelujah, Rufus
Mrs. Robinson, Simon and Garfunkel
Take Me Home Country Roads, John Denver