Have some additions to the list for you. I found the last official Gummy ROM d2lte build over on XDA. It is Android 4.4.4. Personally, I think it really sucks that Team Gummy was forced to stop making ROMs. Gummy was one of my favorites. Even though, there won't be any updates after the last build, it will be stable enough for a daily driver.
Another unofficial Dirty Unicorns 8.1 d2lte build was made. This time by a dev named Kasey Jones. That makes 3 unofficial d2lte 8.1 builds for us by 3 different devs. It's cool they are still showing interest in the GS3.
I added an app called MirrorEnabler. It actually works on every Android rooted device. KitKat comes with Chromecast support built-in. This means you do not need the Chromecast app to cast media using Netflix, Hulu Plus, Play Music, etc. Every ROM on this list has Chromecast support built-in. With the Chromecast support, KitKat is also supposed to be able to mirror your display to the TV through Chromecast. But, that function isn't included in these ROMs. With MirrorEnabler, you'll be able to mirror everything on the display of your smartphone/tablet to the TV through Chromecast. If you use Titanium Backup, or any other app like that, to backup/restore your apps, you will have to wipe the data for MirrorEnabler then open the app to enable mirroring again.
Lastly, I added 2 Android 5.0 GAPPS packages I found. They will work for us because these are Android 4,4,4 ROMs. I'm currently using the 10/28 package but did get confirmation the 10/30 package works as well. You will be able to dirty flash each GAPPS package or just flash them when your flashing a ROM.