Never mind, it's started happening again after resetting preferences. I did some digging and it seems the "premium extensions" (things like the Amazon Assistant promotion) are the source of the crashes. Deleting the key ui.premium_extensions from the Preferences file allows the browser to start correctly, but it will recreate that key on startup so it'll crash the next time.
This is what the key looks like in my preferences:
7963bd3e-b5dd-4730-a3d2-97213bae8321-image.png
Both extension ids are related to the Amazon Assistant popups on Speed Dial and when visiting amazon.com.
I assume resetting my settings only worked temporarily because Opera pulls premium extensions from the servers periodically; I didn't get the Amazon promotion until a few hours ago and that's when Opera stopped working.