I cheated - I connected my phone via USB to my computer and copied the whole DCIM folder from my Phone storage to External/SD storage (and, for safety's sake, put a copy on my PC as well, even though it ends up in Dropbox anyway).
Once it was completely copied, I first disconnected then rebooted the phone, re-connected it to my PC, deleted the Phone storage DCIM folder, went into Camera, Gear - Gear - Gear - scroll down - change Storage to Memory Card.
Rebooted the phone again and made sure the Gallery was the first app I opened. Everything showed up correctly.
