Reading the man page with care, it says that
update_info takes data in whatever format
dump_data generates. That presumably would have to be adjusted according to the page shuffling. Doesn't sound impossible, but automatic it isn't.
The PDFtk site only gives the above hit and creating/editing bookmarks as results. All Google knows about the matter of bookmarks in PDF and reorganizing, is hits on the above operations and lyrical expositions on the marvels they offer, and this thread ;-).
So it seems it can't be done. The comments suggest some possibilities, which didn't work when tried.