Thank you for the reply, my issue was actually solved for me by someone else! I'd like to post how here though, for anyone else suffering from the same issues.
So, I had disabled the GOG overlay, but it turns out I was disabling the wrong one. If you open the Galaxy client, in the list of your installed games, there is a little cogwheel that opens a general settings window. In this, there is an "In-Game Overlay" option under the "Features (Coming soon)" tab. This is what I originally disabled.
The option that I /needed/ to disable to fix the game, however, is a Witcher 3 specific option, which I did not realize. If you click The Witcher 3 in your game list, and click "More" next to the play button, you will get a little menu. Click "Configure" from there, and a new screen comes up. This will have a section labelled "DLCS INSTALLED", and Game Overlay is one of them. Turn that off, and you should be good to go.
I still have both of them disabled, so I don't know if the first option means anything, but I have not had any crashes since then! Hopefully this helps other people.