I was able to get around it (sorta) by switching over to the unpatched version of the game. The wedding plays out with some of the dialogue unsurprisingly a bit wonky (I've got a gay marriage set up with Komari and in the ceremony names were weirdly switched, my character was called the groom once or twice, stuff like that) but doesn't crash or anything. From there I saved, repatched the game, and things seem to be a-ok.I just tried to replicate the issue and got the same thing. I have no clue how to fix this honestly… only thing I can think of is doing the instant marriage cheat for this.
This isn't the only place I've encountered these blackscreens actually, though it was the first time it was almost a softlock. As best I can tell it might be the fault of the Inari same gender part of the patch as all places I have gotten the black screen with music have involved Inari. Spots other than the wedding were Inari's 4th event (the 2nd love event) and when trying to view the first Inari special card in the bookshelf.
Hopefully that helps anyone else that encountered this issue! I'm more than happy to send along my save to anyone interested in looking into it further, just let me know.