So basically I have to handicap my powerful 1070's performance to properly record a screen. Makes sense.
No, you need to allow for OBS to use it. OBS needs GPU to render the frame you're capturing, and then either CPU to compress that frame (if you're using x264) or access to the hardware encoder on the Nvidia card if you're using NVENC.
For any game capable of using all of your GPU's capacity, you'll never be able to stream it at the same quality as you could play it without streaming, since OBS needs some of your computer's resources to work.
1080p60 streaming is challenging for any rig. Trying to also play at a higher refresh rate than you're capturing makes it harder, and playing at a frame rate that isn't an even multiple of your capture rate can also cause problems.
If you're just doing recording, have you tried Shadowplay? I'm guessing they have some ability there to ensure that the game and the capture program share the GPU without competing, given that the devs control both bits of software in that situation. (It's been awhile since I used it, though, so I don't know for certain.)