The majority of lifters using and writing about WSB are equipped lifters and have found that heavy overhead training isn't as worthwhile as other max effort lifts.
I think there was some stuff in the old WSB videos (as in VHS tapes- super old) where they did max effort seated presses and pin lockouts, I know I've seen pictures of Kenny Paterson doing them.
I know quite a few strongmen who train on Westside-inspired programs that use overhead work.
Remember that just because something is a weak link, doesn't mean you have to address it with max effort work. Strength can be built in ways other than 4-7 singles above 90%. From a risk-benefit standpoint, you're probably better off using more specific movements for max effort and using military press as an assistance lift.