I could not get 15.04 to stop hanging, so I switched back to 14.04.
I managed to make 14.04 work when I saw an "Advanced Boot" option under the boot option during the initial UEFI options menu on boot (like the BIOS menu, you just hold down a key like delete
or whatever your computer uses to open the menu on boot). In the Advanced Boot
options, it turns out I could choose the bootloader installed on the ubuntu partition. That bootloader correctly showed ubuntu alongside the windows loader, so I have the option to boot into either.
I'm still not entire sure I understand UEFI and it's various idiosyncrasies, but for anyone having a similar problem, I suggest looking for an Advanced Boot option or something similar in the UEFI options menu.