Magic Mouse 2 must be reconnected after each reboot in Bootcamp

I have 31 just out of the box iMacs on which I need to install Bootcamp. Everything goes fine, except from the moment Windows starts installing the Magic Mouse 2 won't work. Once Windows is completely installed and I go to Bluetooth devices, remove it (it does see it, it just won't work), then add it back it works...until you reboot, when you have to go through the same remove/re-add steps again. Sometimes you do have to turn the mouse off and then back on before it will reconnect, sometimes not. I've noticed no pattern for that. I have never noticed that it just stops working after some time has passed--all that I've ever noticed is that is stops after a reboot. It doesn't stop between users signing in/out. Both the keyboard (which works every time without issues during the Windows install) and the mouse show up in the device manager as HID devices. The keyboard has sometimes quit when I'm messing with everything trying to get the mouse to work, and the same situation applies here as the mouse--it sees it, but removing and adding it back makes it start working again.

Here's what I've tried or that doesn't help:

• Updates are current on both the Mac OS and Window 10 side.
• I've manually downloaded the Bootcamp drivers as described in HT204923 and installed those. It seems to install some video drivers, based on the appearance of the screen, but it doesn't do anything with the mouse.
• I've talked to Apple Support to make sure there aren't any new, but not yet available, updates to Bootcamp and to see if they can help. They say there are not any additional updates, and that it's a Windows issue. (And predictably, Microsoft says it's a Mac issue).
• I've looked for the "Allow the computer to turn off device to save power" options. The Power management tab is not there on any items under Bluetooth, nor on the Bluetooth option under network. It is there on the mouse, but it's already unchecked, although grayed out. But again, I don't see this as the issue, as it doesn't just periodically quit--only at reboot.
• I've run Apple Software update in Windows- says no updates.
• This has occurred exactly the same on the first 10 out of the box iMacs--I'm doing four at once, and just didn't realize it was happening for a while. I thought once I connected it, it was fixed. I was wrong.

If anyone has any ideas, I'd sure love to hear them. I need to get these in a lab, but there's no way I can expect students to use the keyboard through all the steps to re-enable the mouse. And it seems a shame to have to use a bunch of third-party, corded mice.