Can I enter the side of the panel *through* the stud?
As far as I know there's nothing saying you can't put strain relief clamps facing the inside of the panel. I'd simply drill slightly oversized holes through the studs, centered on the knockout, to allow installation of the clamp. Say 1-1/4" for a 3/8" clamp, then run wiring as per usual. 

You could also use snap-in, self-clamping bushings that require no screw tightening and insert them from through the stud or from inside the panel. 

Since the wiring is centered on the stud, as it would be anywhere else in the house, no protection would be necessary.