Where about does the noise come from, Front wheel, Rear wheel, Bottom Bracket ? to me it sounds like metal being forced to rub against other metal. Does the noise happen when the cranks are spun backwards ?
When I'm riding it, it sounds like it's coming from between the BB and the front wheel. When I try to cause creaks while off the bike, like in the video, it sounds like it's between the BB and the
rear wheel. Go figure.

I also didn't hear any loud creaks when I spun backwards.
Regular "ticking" might be a loose spoke!
If I squeeze my spokes, they do make a small ping or 'click' noise, but it sounds different from the noise in the video. Are loose spokes able to make a really noisy creaking sound?
If you stand up and pedal, does the creak stop?
Nope, it gets louder as I apply more torque to the cranks.
If it creaks seated or standing, does it creak while pedaling or while rolling? I'll guess it doesn't creak while sitting still. If it creaks while not pedaling, try tightening the skewer. If that doesn't do it, try a drop of oil on the NDS rear spokes where they cross. if it creaks only while pedaling, is it a cyclical noise - like every rotation of the crank? If so, try pedaling with one leg at a time and see if you can isolate to one side or the other. Loose cranks could be it, but it could be a pedal as well.
When I'm pedalling, I get a more high pitched creak that occurs whenever I'm applying torque to the pedals between 1 and 5 o'clock. I don't have clipless pedals, so I'm not sure if they would be noisy when pulling a foot up. When rolling, I get an irregular staccato creak that is a bit quieter (it sounds like the creak in the video). This mainly occurs when I hit bumps, and sometimes when I'm coming to a stop. I've tried oiling the spokes and tightening the skewer, neither seem to make any difference. I've greased the skewer as well. I don't think it's the pedals, as I can get a creak by gripping a crank arm, pushing downwards, and then rolling the bike back and forth.
Ride with no hands on the handlebars - does it still creak?
Afraid so!
to test just the crank, get on the bike next to a street sign pole you can hold onto... while stopped, stand tall on the pedals. put one pedal forward so the crank arms are horizontal, and bounce your weight on them, then backpedal so the OTHER arm is forward, and bounce your weight a bit again, repeat a few times. does it creak when you do this? if so, its highly likely to be the bottom bracket or the crank attachments, especially if this bike has square taper cranks.
I wasn't able to create any creaks by bouncing up and down, but this was because the front suspension was taking all the damage.

But I could get a creaking noise if I applied heavy pressure to the front-most pedal. Is there any trick to narrowing the possible cause to either the BB or the crank, outside of buying a new one of either?
Thanks for all of the replies so far!