Along the same lines (updated pop arrangements of corny carols) – add The Temptations version of Rudolph the Red-Nosed Reindeer. You’ll thank me later.
Yes, it’s sacrilege to even consider anyone but Eartha Kitt for this song.
Marry Manilow and Pamela Holt for Baby It’s Cold Outside, I think.
Make that Barry Manilow.
Baby It’s Cold Outside - Believe it or not Steve and Eydie’s version of this is absolutely wonderful. As a longtime married couple they are so comfortable together in this song it’s beyond charming.
Santa Baby - I realize Eartha Kitt is going to win this one hand’s down. But Madonna’s version, coming on top of her ‘Material Girl’ mode and delivered in a baby doll voice really did some good things.
I’ve got a CD that has a version of this song by Dion that is really pretty good.
The same CD also has a surf-rock version of Frosty the Snowman by the Ventures.
For some nice late 80s schmaltz, Alexander O’Neal’s The Christmas Song.
And my vote,** Fairytale of New York **by the Pogues and Kirsty MacColl. Remakes? The Irish Tenors did a cleaned-up version of it. 
I’ve always preferred Tommy Smothers’s version of Santa Claus Is Coming To Town:
You better watch out,
You better not cry,
You better not pout -
I’m telling you why:
Santa Claus is dead.
I’ll use this thread as an excuse to post this again:
From the songs on your list, I like this live version a lot.
Please Come Home For Christmas - Holly Cole (live)
This is from the same concert. It may or may not be too weirdo for you. I love MMOH to death, but her odd way of singing is for most an acquired taste:
White Christmas Mary Margaret O’Hara (live)
There are tons of songs not on your list I’d love to recommend, but I have no time. Here are a few though.
“Home For Christmas” - Kate Bush
“December Will Be Magic Again” - Kate Bush (alternate “Kate-dancing-in-a-chair-in-her-jammies Bongo version”)
Here’s a simple, very traditional version of “I’ll Be Home For Christmas” by Rebecca Jenkins from that same concert above.
This might be too “novelty” for you, but it always makes me smile and bounce.
“Blue Christmas” - Danielle Dax
White Christmas is a toss up between The Drifters or Barbra Streisands. Even though I’m leaning more towards Barbra Streisand’s version.
Wow! Would she happen to be the daughter of Leon Redbone and Janis Joplin?
Ha, no, but she is the sister of the actress Catherine O’Hara.
What they said.
“The Christmas Song” - Bing.
“Winter Wonderland” - Harry Connick, Jr.
“Sleigh Ride” - The Boston Pops or any other Leroy Anderson arrangement.
“Rudolph” - Jewel or Bing Crosby & Ella Fitzgerald.
“Silent Night” - The Music City Brass.
I think the Jingle Cats do most all of these.
And to preempt your criticism, the Jingle Cats are not a parody band, they are a tribute band made up of deeply spiritual cats!
This is probably the most unusual treatment of Midnight Clear I’ve ever heard. The actual singing starts at about 1:17, but the instrumental lead-in is great.
Definitely agree Frosty the Snowman in fact the whole dang album Christmas Islandis very good.
Lest we forget… Christmas in Prison by John Prine.
Frosty non-traditional but nice.
Baby it’s Cold, Ray Charles
White Christmas Bing or nothing
The Christmas Song Many to chose from, not too many people screw with it. Judy Garland.
Santa Claus is Coming to Town Arthur Treacher from the old Merv Griffin Show Really puts the menace into the song.
Please Come Home for Christmas Darlene Love (Baby Please Come Home?)
Santa Baby Eartha Kitt.
Frosty the Snowman - from this cartoon, with an a capella pop chorus. Frosty the Snowman - YouTube
The sound probably isn’t up to your desired standard, though.
I found this live version of Holly Cole singing it. The music is way too jazzy for my tastes, but Holly always has fun.
Disclaimer, I’m biased for Holly no matter what she sings. I met her when I interviewed her for my radio show. lissener and I picked Holly up from her hotel during a snowstorm (she was quite amused when I tried to cover her head with an umbrella. Apparently no one uses an umbrella during snowstorms in Toronto?) We went to Ann Sather’s Restaurant and the management set us up in a banquet room upstairs. We set up the audio equipment and spent about 2 hours with her. She’s so funny and sweet and warm. We had a great time!