I do know which song is which when I hear them, but I dont have a list rn since I picked them at like 3 am before the day of release, lol.
The one in burning basement is Rebel Yell https://www.youtube.com/watch?v=a3z8LSmFhmg
Still, Turbo has some neat songs in there that are not in this mod, I'd say check them out and maybe you find something else you like.

my hero, thank you very much

Me and my friends did some listening and guessing and we got them all

Stage 1/2 [Basement]:
Dota
https://www.youtube.com/watch?v=dwpMXtt8wBo
Stage 1/2a [Cellar]:
Kickstart My Heart
https://www.youtube.com/watch?v=6A5ku3bPoH8
Stage 1/2b [Burning Basement]:
Rebel Yell
https://www.youtube.com/watch?v=a3z8LSmFhmg
Stage 1/2c [Downpour]:
Careless Whisper
https://www.youtube.com/watch?v=X8SiGTjCT2o
Stage 1/2d [Dross]:
crossing field
https://www.youtube.com/watch?v=vhrpNB-cvJM
Stage 3/4 [Caves]:
♥♥♥♥♥ Lasagna
https://www.youtube.com/watch?v=nuEQU3nxClY
Stage 3/4a [Catacombs]:
Stoneocean
https://www.youtube.com/watch?v=dePkTaf-cfM
Stage 3/4b [Flooded Caves]:
Dragostea Din Tei
https://www.youtube.com/watch?v=tcCLgi5VDUk
Stage 3/4c [Mines]:
Revenge
https://www.youtube.com/watch?v=x9U9phVAnUg
Stage 3/4d [Ashpit]:
The Bad Touch
https://www.youtube.com/watch?v=3i9pUGPCq9I
Stage 5/6 [Depths]:
Black Rover:
https://www.youtube.com/watch?v=-iuBn2svtkM
Stage 5/6a [Necropolis]:
Säkkijärven Polkka
https://www.youtube.com/watch?v=vivZ2Q841MQ
Stage 5/6b [Dank Depths]:
Uragirimono no Requiem
https://www.youtube.com/watch?v=N-sEZ4jkXpg
Stage 5/6c [Mausoleum]:
99.9
https://www.youtube.com/watch?v=rLTgUQxYnBI
Stage 5/6d [Gehenna]:
YOU WA SHOCK
https://www.youtube.com/watch?v=eCMg3oGb5Co
Stage 7/8 [Womb]:
Maneater
https://www.youtube.com/watch?v=yH5rzZd_a9Y
Stage 7/8a [Utero]:
Fortunate Son
https://www.youtube.com/watch?v=piLhYZGEtEU
Stage 7/8b [Scarred Womb]:
Maniac
https://www.youtube.com/watch?v=_Cn0LchHgkw
Stage 7/8c [Corpse]:
Astronomia
https://www.youtube.com/watch?v=sR8c3ugaSKM
Stage 9 [???]:
Gurenge
https://www.youtube.com/watch?v=xw33cS7AH40
Stage 10 [Sheol]:
Clattanoia
https://www.youtube.com/watch?v=wK9ACmuCGrE
Stage 10a [Cathedral]:
A Cruel Angel's Thesis
https://www.youtube.com/watch?v=-91KYz8ClBQ
Stage 11 [Dark Room]:
Kiss of Death
https://www.youtube.com/watch?v=HHxmT8dhVQo
Stage 11a [Chest]:
Fantastic Dreamer
https://www.youtube.com/watch?v=XhvmG0fwEeo
Stage 12 [The Void]:
Holding Out for a Hero
https://www.youtube.com/watch?v=uh2jT8czl3o

I think you only missed the one for the one that plays on the trip home, which is this one:
https://www.youtube.com/watch?v=Zp5NMBJTd18
But awesome job!, Im pinning this one.

Made this a playlist and also added some missing tracks (will add more tracks as I add them to the mod)
https://youtube.com/playlist?list=PLaTEv8slEbwtYz1IM0jVURDWRoRmdtucT