(Er, spoilers here. I don't think anyone else is using tags but it's worth asking?)
Yeah, I'd lean towards the broadcast having some ongoing effect if anything. Just thought you guys had ideas for the plot already so didn't comment. The crew knowing what happened unlike canon (were their memories wiped in the actual movie?) might actually bring them closer together. There's not any ways to resist mind control in One Piece, otherwise I could see them being determined to learn it.
Robin is very unlikely to defect now. The slip of her name in the broadcast seemed like a plot hook as well.
The encounter with Moriah could definitely be different from canon - Luffy definitely won't be underestimated this time. Garp I can totally see repressing the event just like Luffy.
The island will definitely be demolished by the buster call but does that mean people will be asking questions about marines being able to destroy islands? Remember that Ohara was pinned solely on Robin which gave her the bounty. I don't think the buster call was known to the public.
I fully expect Sabo to track down Ace and Luffy (or at least send a snail call) but given your original plots of canon you surely already have plans for that.
I do share EVA's concern about lack of (warning tropes)
In Spite of a Nail - TV Tropes but this story is so entertaining that I actually don't mind it too much. Before this event, Cross and the Strawhats didn't have much credibility. Now that Sengoku gave him the offer and his family revealed to the greater public, the changes are likely to start piling up.