I was going to call this a Christmas mix, but given that there are songs about New Year and Hanukkah, and several generic “winter” songs, this is The Sci-Ence! Justice Leak! Generic Winterval Holiday Mix
Tracklisting:
I’m Walking Backwards For Christmas — The Goons
Happy New Year — Beverly
Back Door Santa — Clarence Carter
Blue Christmas (To Whom It May Concern) — Miles Davis
Snowflakes — The Honeys
We Three Kings Of Orient Are — The Beach Boys
Santa Claus Is Coming To Town — Little Richard
Rock & Roll Winter — Wizzard
New Year Carol/Residue — Waterson: Carthy
I Wish It Could Be Christmas Every Day — Frank Sidebottom
Wonderful Christmastime — Paul McCartney
White Christmas — Charlie Parker
Shake Hands With Santa Claus — Louis Prima
I’m Spending Hanukah In Santa Monica — Tom Lehrer
The Santa Claus Crave — Elzadie Robinson
Auld Lang Syne — The Beach Boys
The spoken linking passages are all taken from I’m Sorry I Haven’t A Christmas Carol!
Sci-Ence! Justice Leak! 
I hope the Beach Boys sang the proper words, viz:
We three kings of orient are,
One in a taxi, one in a car,
One on a scooter, blowing his hooter,
Following Ringo Starr
(btw I think your novel *would* work as epistolary. Most important thing is to write in a style you’re comfortable with.)
I *think* you’ll find the words are
We four Beatles of Liverpool are
John in a taxi, Paul in a car
George on a scooter, tooting his hooter,
Following Ringo Starr
Sadly on no Christmas album I know of do they come close to singing the right words — the closest is Frank Sidebottom’s Xmas Medley, which uses your lyrics but with the last line “travelling far like jam in a jar”.
Nor, for that matter, do any of them seem to have the proper lyrics for Good King Wenceslas (“Good King Wenceslas looked out/of his bedroom window/Silly bugger he fell out/On a red hot cinder/Brightly shone his arse that night…”) or Jingle Bells (they all make it about sleigh rides rather than Batman, which seems to me to miss the point).