Hi Kyra thanks for sharing your progress with us!
Everything's looking a bit stiff to my eye. There's a few things that typically contribute to this:
Materials too stiff
Over constraining (too many attachments)
Tet resolution too low. (not enough degrees of freedom to represent shape change)
I'd just start again with the brachiocephalicus as that's an important muscle and isn't performing quite right in your scene.
Looks like it's attached to the scapula which is what's pulling it up and through the neck. And then it's also tightly attached to the sternomastoid which is coming along for the ride and buckling.
For authoring I usually just start with the animated bones and add one muscle at a time. Get the performance approximately right and then add another. Try to be conservative with attachments i.e. get as far as you can with just the origin/insertions, zFibers and default materials. Then you can add soft attachments between muscles and other muscles/bones if you're finding there's too much jiggle or they're deviating from the expected movement.
Don't forget inertial damping on the zTissue node for each tissue which can take out a portion of the world space inertia out, so that the secondary motion isn't so wild.