Ubuntu – How to perform do-release-upgrade from 15.04 to 15.10 once 16.04 was already released?

This is more of a redirect, but when I posted my broken package issue on launchpad (similarly trying to upgrade from 15.10 to 16.04), I got excellent support. In my case my issue was that I had used a foreign source (a ppa) to install some more recent graphics packages, specifically libgl1-mesa-dri, libegl1-mesa, and libgbm1. I had to downgrade those packages to the Ubuntu source versions, and then I was able to proceed with the upgrade. So my suggestion for handling broken package issues is to follow the steps in the OP, e.g.

sudo apt-get update --fix-missing
sudo dpkg --configure -a
sudo apt-get install -f

and if that fails, consider whether any ppas might be introducing package versions that would interfere with stock Ubuntu packages. Additionally, if you get extremely frustrated (like I did), get support on Launchpad.