Well, it can be fixed - but not easily and not nice.
Looking at the code, music ID 43 is indeed loaded (that's what FH concert uses too) - and also which full tune you played (Irish Jig / Eyes on Me) will be the one played. I am not sure how the latter works in code. It doesn't work like the other music. ID 43 doesn't stay there long - it's superseded by ID 10 (an unused ID).
I can add in a crappy hackish work around, where you manually place Irish Jig or Eyes on Me as the music and, once the statue is complete, they will play. But even that isn't perfect because the PC version changes the music again depending on which house you go into. It would certainly be better than nothing, of course. The bottom line is - without someone editing the script, it will never ever be perfect. Same with the sound effect issues.
The PC port team simply didn't bother correcting this part of the game.