Oh that brings back memories of that feeling of relief when baby drained a full-to-bursting boob. Feels so good LOL. Yeah, pump away. I pumped heaps when Kayla was prem.. I would get 200ml+ in 5 mins each side. It didn't seem to affect my supply that much, nor cause any issues once I stopped pumping. As someone said earlier, it's all hormone driven at the moment, not really on supply/demand. Be careful with manual massaging if they're feeling that full, you can bruise/damage the ducts. I would think it best to just pump/feed baby.

I also wouldn't worry about having to drain each side completely. Your body is obviously in overdrive as the milk comes in.. she doesn't have to drink it all. I've not been one to record or count which side we're up to or how many feeds etc. I would just feel which boob felt fuller and go with that. Use baby to relieve whichever is feeling like it needs to be drunk from and then just make sure it's a decent feed before swapping. I found if the feed was too long on one side and then I swapped, she would only have a quick feed.. enough for let down, and then not need any more and I was left with a full boob :/