1. "Overture"
2. "Fathoms Below"
3. "Wasting Away"
4. "Part of That World"
5. "Part of Your World (reprise)"
6. "Under the Sea" (before Triton destroys her grotto, not after, and no reprise)
7. "Her Voice"
8. "Poor Unfortunate Souls"
9. "Beyond My Wildest Dreams"
10. "Les Poissons"
11. "One Step Closer"
12. "Kiss the Girl"
13. "Poor Unfortunate Souls (reprise 1)" (Ursula transforms into Vanessa)
14. "If Only (Duet)" (the point at which Eric is about to give up on the mystery girl, just before he's entranced)
15. "Poor Unfortunate Souls (reprise 2)" (Vanessa in front of the mirror)
16. "All Good Things Must End"
17. "If Only (reprise)" (by Ariel on the rock watching Eric after everything's over ending with them kissing on the beach)
18. "Finale Ultimo"
Also, I would've brought back the deleted "Fathoms Below" from the making of the original film that talked about Ursula being Triton's sister and her "wicked dreams" since they went full steam ahead with the whole sister backstory in the show.
I actually never loved "Wasting Away" as much as others here back then, I always enjoyed "I Want the Good Times Back" more aside from the preliminary stuff about her and Triton's father; I really love all the stuff about her longing for the past and the climactic lines "The trident, the crown, the throne--the whole damn works. But most of all I want ol' Triton pinned and wriggling on the rack." I actually like the way they mirror Ursula's "I Want" song here with Ariel's... Ariel just wants to live her life and experience life above, whereas Ursula wants things--everything, lol. And even the way she ends the song, with the way she sings with certainty that the good times are coming back, it's similar to Ariel on the rock deciding she will find her way to Eric one way or another.
But since IWtGTB ended up being excised later on in the show's run and overseas anyway--I believe?--it would've been better to have just stuck with "Wasting Away" if it meant we got AGTME. I lovelovelove "All Good Things Must End," although come to think of it now I can't really imagine Sherie Rene Scott pulling it off. Or simply have no song where "Wasting Away" / "I Want the Good Times Back" would go at all.

Sorry, I don't have a link for "Her Voice (reprise)." When the early start of the show began, they had some leaks with Boggess, Scott, etc. and the other actors. I have a recording saved, it may be on YouTube somewhere for all I know. It comes a little ways after "If Only." Triton has just learned where Ariel is, Ursula must be watching Ariel from her bubble:
"Now at last my plan is on its way to its delectable conclusion
Only one more sunset and then finally I'll own the little minx (or niece??)
Soon I'll have my brother just exactly where I want him
And I'll be unstoppable as long as I have this--her voice, ha"