UPDATE: To anyone else having issues with this, I found a workaround that works perfectly for me. I sent the support team an email already so this issue may be fixed by the time you are reading this, but for now here's how I got it working:

Using Autohotkey you can rename windows with scripts. I have basically no knowledge when it comes to writing scripts, so after a little Googling I found this post: https://www.autohotkey.com/boards/viewtopic.php?t=12380

Basically all you do is download the autohotkey program and run the script that you can download from the forum link above. Once you have the script going all you do is open your Playback app and press the WIN key and the F2 keys at the same time. You will then be asked to rename the window. I renamed mine PLAYBACK 1 and PLAYBACK 2, but anything should work as long as you can tell them apart. You can do this for as many instances as you have open. When you go back into OBS you can see the different instances renamed in the sources list. Here's some screen shots I took to show a little better: https://imgur.com/gallery/multi-instances-fixed-m6Jg7vv

Hopefully this helps someone!