Sorry little late on this, but i managed to solve this for myself about 5 minutes ago. I'm using it to stream classic consoles. Within the elgato software this means my resolution was set to 720p. I had also unchecked the "allow 60 fps" because a SNES doesn't need 60 fps lol.
My OBS kept crashing when using elgato in Win 10 like yours. Here's what i did.
Step 1: Open elgato software and make sure your console is running through it properly. IMPORTANT: Do NOT close the Elgato software.
Step 2: Open OBS and go to your elgato properties. Match as best you can the properties you have set in the elgato software. Meaning i had 720p in elgato so i changed it to 720p in OBS. I also changed it from 60fps to 30fps.
Step 3: Preview Stream. Because the elgato software is already running in some capacity OBS should not crash. It will show in Preview that it's being used by another application but that's okay. At least you started without a crash.
Step 4: Close elgato software. OBS should register this change. It may look frozen for just a second, but it should resume with working gameplay.
After i did this, i was able to turn of the preview, turn off the console, and restart the preview with a new SNES game. I did my best to explain exactly what i did, so i hope it works for you as well.