I'm not sure how much this helps everyone, but it's finally stopped for me.
One thing that might be of importance: I had an iOS beta profile on my iPhone. That was removed a few weeks ago, and I was prompted to update to the formal iOS 10.3.2. release about 10 days ago. Since then, the double notifications have stopped.
Important to note that my problem was exactly as people described: I was receiving Calendar notifications, despite deleting it and defaulting to Fantastical. This persisted, even after a restore as new on both my iPhone 7 Plus and Apple Watch. I'm assuming the iOS beta lingered on my phone after the restore, because it's been all peaceful since I updated to the official 10.3.2 release.
I also did have a lengthy chat with a few Apple reps. I can't promise they didn't work some magic on their end, too, but Fantastical has been my only calendar notification since.