But the poor little stub... there's about an inch of trunk/branch peeping up above the soil. I literally just planted it a couple of weeks ago, so I was Really Sad about its destruction. Do you guys think it might survive? Is there anything I can do to help it pull through?

My dogs are 180-200 lbs. and the puppies are very clumsy and the cages do work.
It's just enough of a deterrent to cause them to go around instead of through LOL.
I buy the fencing in bulk and cut to fit.
When the plant reaches a size where it can hold its own I cut the cages off and discard them.

I also think it is important to keep some paths clear.
My beds have room between the fence and the plant farthest back for the dogs to run.
They're gonna do it regardless so I just incorporated that thought into the bed designs.
And everything is dog proofed- even those reindeer there are impaled on steel fence posts driven deep.

As far as your damaged plant, cage it and watch it- that's about all you can do.