@scholasticus First thing to understand is that corgis are high energy dogs. They're herding dogs and need to have that energy worked on everyday.
Cut down on the physical exercise, contrary to popular belief,a lot of physical exercise just increases the dogs energy so they can keep up with it, start looking into some mental stimulation like obedience, scent work and obedience exercises. If you can tire a dog out mentally then the body will follow!
Games such as fetch and going to the dog park are actually super arousing to a dog, cut these down or maybe stop for a while.
I've heard about the relaxation protocol but haven't gone all the way through with it, but the process is teaching your dog to basically chill out on a certain spot.
If she keeps breaking position and can't sit still put a leash on inside the house and tether them to something when you are busy for short periods of time. Constantly reward for any calm behaviour and ignore for behaviour you don't want (don't use punishment as if used wrong can damage the bond with your dog)
Scavenging, you can either give something else to do like a chew toy or a Kong with food or something. I found that if Jasper was bored he'd sniff around until I either stopped him, played with him or gave him something to do.
As for the biting, keep her away from your face, as you work on bite inhibition.
Promote a calm environment and only get her excited when you want to initiate play but then keep her calm the other times. Give plenty of mental stimulation and avoid from getting bored!!