What can I do when "Find My iPhone" won't turn off?

I've been trying to restore my iPhone SE (running iOS 10.3.1) from a local iTunes backup, but iTunes on the Mac says that it cannot preform a restore until I turn off the "Find My iPhone" feature. I've been repeatedly trying to do this, but to no avail. I also tried restarting the iPhone or doing a hard reset between attempts. When I try to turn the Find My iPhone feature off via *Settings > Apple ID > iCloud > Find My iPhone,* the screen shows one of three things: 1. The slider moves to the Off position, but when I return to the iCloud page, the Find My iPhone line indicates that the feature is still On. (If I return to the Find My iPhone page, it indeed shows the slider as On.) 2. A prompt appears, asking for my Apple ID password. Entering it doesn't do anything (obvious). 3. Like # 2, I get an Apple ID prompt. Entering it just leads to an error message: "Verification Failed: There was an error connecting to the Apple ID server." However, when I check Apple's System Status web page , all of their services (including Apple ID and iCloud) are in the green. I've seen other questions asking how to turn "Find My iPhone" off, such as [this 2014 question](https://apple.stackexchange.com/questions/123640/how-do-i-turn-off-find-my-iphone-on-my-device-without-wi-fi) which asks how to do it without wi-fi access, but I haven't seen anything that addresses my specific scenario. Has anyone else resolved an issue like this? What else can I try? Any idea why it is happening?