I'm not familiar with the NAS, but if you can run wget, perhaps you can try youtube-dl, instead? Otherwise, I'd pursue what Mark suggests -- why involve YouTube at all?

I checked out the stream. I could rewind to 8:04am, where there was a gluttonous seagull pacing back and forth on the railing. It ate the majority of what food was there. A crow got one piece of food, a squirrel got two pieces of food, and then another seagull came and ate the rest, and tried to dump out the water to spite anyone else. The food was gone by 8:40am. If this is normal, I don't think you can say you're feeding the crows... you're feeding the seagulls.