A good many folk songs – from various parts of the British Isles, anyway – share in this trait. Their makers plainly had fun making the choruses long, agglomerative and complicated. One of the more tongue-twisting of such songs is an English one, “The Mallard”. I have trouble doing direct links; but googling “The Mallard Song” will bring up “The Mallard Song – You Tube”, with a bespectacled bearded guy in a baseball cap singing the piece in question.
I’ve never found Wipeout available for karaoke.
“Cry If You Want” might be a good example:
Don’t you get embarrassed when you read the precious things you said
Many many years ago when life appeared rosy red
No one ever shared your bed
Nothing ever filled your head
Except yourself and little Ted
If you’re going with Lehrer, you need to mention “The Elements.”
I’m always amazed by Daniel Radcliffe’s version.
From Sondheim’s Into The Woods:
Rooting through my rutabaga,
Raiding my arugula
Also from Lehrer, this bit from When You Are Old And Grey:
An awful debility,
- A lessened utility,*
- A loss of mobility*
- Is a strong possibility.*
- In all probability*
- I’ll lose my virility*
- And you your fertility*
- And desirability,*
- And this liability*
- Of total sterility*
- Will lead to hostility*
- And a sense of futility,*
- So let’s act with agility*
- While we still have facility,*
- For we’ll soon reach senility*
- And lose the ability.*
Although, to be perfectly honest, few of these songs are particularly difficult to sing, as long as you actually know the words and how to pronounce them. The Lobachevsky bit in the OP isn’t hard, and Pick-A-Little is downright easy. As for my contribution, the tough part is to remember to take a big enough breath!
The Aristotelian version is perhaps more karaoke-friendly.
I’m going with a speed rapper, namely Twista.
His name used to be Tung Twista. Can you guess why?
“I Want You” by Savage Garden.
Putting On The Ritz
“Third Uncle”
Just try to sing along. 
Royals. Just try to sing that laundry list in the chorus.
The Dead Kennedys - Drug Me
That version is bad enough, but the song was originally Australian, and the words are even more foreign to everyone else. Try singing about your visits to Woolloomooloo, Maroochydore, and Yeerongpilly.
Bauhaus managed to cover Third Uncle.
Well, try to sing the last part of “The Elements”–beginning with “argon”–real fast, and see if you don’t stumble. Hard, eh?