Ok I realise this thread is quite old now, but this bug is still a problem which I also got. However I have somewhat of a 'fix'. Although the story doesn't actually appear the item (whether spice crate or music box) is still buried on the island, so both the items are there. So it is possible to obtain them. My solution was to look at the RareThief Wild Rose guide and find all the islands which could have the item on and as they detail where you need to dig on the island you simply go around to each island and dig where it is supposed to be. Using this method I managed to get the spice crate by finding the 4 possible islands it could spawn at and going to them and digging in the rough area, it worked the spice crate was there even without the story.
This is a bit of a crude method because it does mean you have to 'cheat' but it is the only method ive found.
I hope this helps other players out who come across this in the future seeing as Rare doesn't seem like they will fix this bug anytime soon