I agree with you Vince, this is why I said that using only compound movements would partially resolve this problem as any pulling exercises will involve the lats, rhomboids, teres, traps, rear delt, biceps, brachialis, forearms, etc while all pushing exercises will involve the chest, anterior and lateral delts, triceps, serratus, etc.
Regarding specialization, or not training equally all muscle groups, I also agree with you on that subject. In fact many of my articles deal with that subject. In my articles I propose training the specialized muscle(s) 3x per week and only performing maintenance work for the rest of the body; rotating the spec muscles every 4-6 weeks.
But I feel that the time constraint of the program might sill pose a significant problem. BTW, I'm not a HIT nor HST advocate so I don't necessarily think that low-volume is the solution.