Building mass is largely a matter of including enough volume and as you mentioned already, eating like a carnivorous horse.
I've run WSB inspired programs, not WSSB but I was and am able to gain mass whenever I program for it. I work up to triples and 5's. I think Defranco has you work up to 5's. Then you do some work for volume. Then you have more assistance work.
I have a hard time imagining how you wouldn't get bigger/stronger while maintaining some athleticism.
As far as only training squat or deadlift any given week, you could choose a supplementary exercise that's a variant of the opposite movement you started with. Like this:
Pause Squat up to 5RM (or if your form is still rough and you need to practice, you could work up to a technical max, that is the heaviest weight you can use before unacceptable form breakdown)
Pin Pulls from mid shin height for 5x10 @ around 50% more or less.