Well, it's the darndest thing but I'm on iOS 9.3.5 after successfully doing a restore! I didn't think this was possible if you had the 'swipe to upgrade' screen happen.

If anyone else happens to be in this situation, the only thing I did out of the usual was reset the phone when it attempted to run the upgrade on the load bar screen, then put it into DFU mode and connect it to iTunes. Nothing else apart from a further reset when I couldn't get anywhere.