I did a frickton of stuff (due to boredom and spare time): unpacked this mod, went on the wiki, opened up notepad++, copypasted music track from wiki to notepad++, copypasted the soundtrack list from this mod page, tried looking up what each song replaced what and only to find out... the tracks listed on the mod page is aligned to the tracks alphabetically listed on the unpacked mods folder. Yeah, I wasted a lot of time doing this but I did find some errors and discovered missing info so I guess it wasn't a wasted effort? Anyways I made a list with stuff I took from the Starbounder wiki and identified the tracks on the mod page to it. Lines with parentheses meant that the mod author just replaced a soundtrack that doesn't play normally ingame (as of version 1.4 AFAIK). Lines with Asterisks are errors made by the mod author.

Dynatron - A Beacon From Home -> Accretion Disc - used at the end of the Miniknog Stronghold mission

Power Glove - Streets Of 2043 -> Arctic Battle 1 - used in the second half of the intro mission and the Miniknog Stronghold mission

Perturbator - Vengeance -> Arctic Battle 2 - used in the Dreadwing the Penguin and Shockhopper MK I encounters

Power Glove - Freefall -> Arctic Battle 3 - used in the Asra Nox and Big Ape boss encounters

Tommy '86 - Back To Basics -> Atlas

Power Glove - Jungle Warfare -> Blue Straggler

Mitch Murder - Power Move -> Crystal Battle 1 - used on the Ruin's surface

Mitch Murder - Enter The Fury -> Cygnus X1

(Lost Years - West Side Lane -> Desert Battle 2 - not used in normal gameplay)

Perturbator & Dynatron - Volcanic Machinery -> Desert Exploration 1

Carpenter Brut - Paradise Warfare -> Desert Exploration 2 - used in Tech obstacle courses

Mitch Murder - Ocean Avenue -> Epsilon Indi

Dynatron - Vox Magnetismi -> Eridanus Supervoid

Power Glove - Trials of the Blood Dragon -> Error 0xbfaf000

Mitch Murder - Melting Point -> Europa

Carpenter Brut - Turbo Killer -> Event Horizon - used in the Challenge Rooms, the Baron's Keep battle and the second Arena fight

Lost Years - Phoenix Rising -> Forest Battle 2 - used in the Heart of the Ruin boss encounter

Mitch Murder - Race Day -> Forsaken Grotto

(Perturbator - Savage Streets -> Gravitational Collapse - not used in normal gameplay)

Perturbator - Welcome to Nocturne City -> Gravitational Collapse (Loop) - used in the Erchius Horror, Ixodoom, Kluex Avatar and Bone Dragon boss encounters and the first Arena fight

Dynatron - The Pulsating Nebula -> Haiku

Dynatron - Descend -> Horsehead Nebula

*Dynatron - Toward the Island Universe (Incorrectly listed as Moon - Dust) -> Hymn to the Stars *

Perturbator - Eclipse -> Impact Event - used in the Ancient Vault boss encounters and the third Arena fight

Dance With The Dead - Out Of Body -> Inviolate

Dynatron - Escape -> Jupiter - used in Player Space Stations

Tommy '86 - Astral Dreams -> Large Magellanic Cloud

Power Glove - Sloan's Assault -> Lava Exploration 1 - used in hostile NPC Ships and Space Encounters

Power Glove - Warzone -> Lava Exploration 2 - used in Ceremonial Hunting Caverns and Fire Vaults

Tommy '86 - Outer Space Adventurer -> M54

Dynatron - Pulse Power -> Mercury - used in the cinematic played after defeating the Ruin

Perturbator & Lueur Verte - Mirage -> Mira

Mitch Murder - Traces To Nowhere -> Nomads

Perturbator - Raining Steel -> Ocean Battle 1 - used in the Erchius Mining Facility

Perturbator - There Is No Love Highway -> On the Beach at Night

Mitch Murder - Frantic Aerobics -> Planetarium - used as in the first half of the intro mission as well as in the Outpost and Koichi's Museum

Power Glove - Katana -> Procyon

El Tigr3 - Bleed Them White -> Psyche

(Mega Drive - Maniac -> Scorian Flow - not used in normal gameplay)

Mega Drive - Night Prowl -> Stellar Acclimation - used in the credits cinematic played after defeating the Ruin

Mitch Murder - Glass Cities -> Stellar Formation

Dynatron - Andromeda Bleeding -> Temple of Kluex - used near the Ark, on Ancient Gateway celestial objects, and near Ancient Gates on Garden planets

(Vestron Vulture - Real Bout -> Tentacle Battle 1 - not used in normal gameplay)

Perturbator - Ghost Dancers Slay Together -> The Eternal Tide - used in the cinematic played upon first meeting Esther Bright near the Ark

Perturbator - Electric Dreams -> Title Menu Music - current title screen and menu music

Perturbator - Last Kiss -> Tranquility Base - used in friendly NPC Ships and NPC Space Stations

*Perturbator - Vigilante 2084 (Wasn't listed in the mod page) -> Ultramarine*

*(Carpenter Brut - Meet Matt Stryker (Wasn't listed in the mod page) -> Ultramarine (Loop) - not used in normal gameplay)*

Dynatron - Aurora Nights -> Vast Immortal Suns

PS: I didn't double check if all the songs on the listed mod page are correct. A few of these songs (i.e. Astral Dreams) weren't on Youtube and Soundhound couldn't verify it. Not sure if the mod author is going to correct the errors on the mod page, or even update the mod itself. Either way, I need to find a better hobby.