If you want to eliminate the TOB sound, (statically), you can loosen your clutch linkage pushrod at the fork, and pull the fork/(TOB) away from the fingers, if the adjustment is close to them. That way you'll know for sure the TOB isn't bouncing off them. Of course you'll have to put the adjustment back to normal. When diaphragm clutches wear, the fingers when relaxed aren't always on the same plane, and will sometimes cause them to hit the TOB, (If the adjustment is tight) and make a noise. But like you mentioned, it's usually more of a chirping noise. If the noise is still there when idling, with lots of clearance, then you'll know it's not tranny or clutch related.
If your input shaft bearing is going, it could make a noise when the clutch is released in neutral, and when the car is in any gear.
And when shifting, (up or down) and you get a grinding noise trying to get it into gear, you could have worn syncros. But I wouldn't associate that with a "whirring" sound, but more of a grinding noise.
Have you checked your fluid level yet? Stick your finger in the fill hole, and see if you can feel oil. If you can't and it's low, maybe you'll have an easy fix. Good luck.