Through a little trial and error I’ve made it work. This probably isn’t the only way, but it worked for me.
1) Install Windows on the beginning of the disk.
2) Install Ubuntu in a subsequent partition. Resize Windows with gparted if you need to.
3) At this point, only Ubuntu will be in the grub menu. Boot the Ubuntu install cd/usb again and install Boot-Repair. See the instructions under “2nd option”: https://help.ubuntu.com/community/Boot-Repair
4) Run boot repair with the default settings. Pray to something holy. Reboot.
And finally, go into the Ubuntu update settings and check only the box for security releases. Updating everything is a recipe for disaster. If your system works, don’t mess with it unless you want to spend a Saturday during ACL troubleshooting nvidia drivers and an xorg.conf.