So there is a grinding noise at idle just like in the video. Push clutch pedal in (even barely) and it goes away, rev with the clutch pedal in and the grinding comes back. While in gear, anywhere above 3k rpm there is a loud "whirling" noise when I let off the accelerator. Goes away as soon as i press the accelerator.

I also took a photo from the inspectors hole of the trans. It is an Exedy Twin.

 

Bump

 

could be a number of things, hows your trans oil look? To me it sounds like its a trans issues, possible bad bearing or slider or worn Shift fork. Any of the gear skip out of gear or are hard to engage? check the trans oil level and oil for shavings.
I say trans cause it goes away when ya push the clutch in, thus making eveything in it stop spinning. givin the fact your not moving of course.

 

Trans oil is at the correct level but I have not looked to see if there are shavings. The car drives fine, goes in gear everytime and no slippage.