So what I was able to do was install Percona, which is a drop in replacement for mysql. They have packages for 5.5, 5.6 and 5.7 available for Ubuntu 17.04. I installed version 5.5 and was able to bring up my database. From there I could upgrade to 5.6 and eventually mysql 5.7. However, somethings still were not working correctly, like emojis were not being stored correctly, so I attempted to fix that, and things broke again. I couldn't start the database and nothing I did seemed to help. Luckly, I made a backup of the data when I successfully had 5.5 running. I reverted everything back to 5.5 and have since upgraded to Percona 5.6. I'm staying here for now. Things appear to be stable and working.
I've got to say, Percona is fast. A few tables that mysql wasn't able to optimize properly, Percona did without any troubles. Right now I'm thinking I'll stick with Percona until I no longer can.
So, attempted to upgrade my server from Ubuntu 14.10 to 16.10. Everything seemingly went smoothly, except mysql. For some reason it didn't get upgraded. No big deal, I thought to myself, I'll just install it. Well, it turns out there's some sort of problem with mysql and Ubuntu 16.10. I Google'd and I Google'd, tried a bunch of different suggestions, nothing worked, mysql just wouldn't properly install.
I'm now in the process of upgrading to Ubuntu 17.04. I looked through the release notes for 17.04 and there's no mention of any issues with mysql, so hopefully this will solve my problem. When there's no way back, you go through.
My first attempt to upgrade to 17.04 didn't go very well. The broken mysql-server packages from 16.10 were still in place and caused the upgrade to fail. That was a treat to troubleshoot and smooth out. I've got it going now though.
On a related note, because my server is down, I can't post this update, so I'm writing it down now and I'll attempt to post it with a "published date" in the past and see if Known accepts it.