As always, @FlatsFarmer speaks and I listen. My only big contribution here is this
Keep in mind that max effort days aren’t “lift heavy days”: they’re maximal STRAIN days.
When it comes to deadlifting, straining is easy. The weight is dead (hence the name), and you pull against it as hard as you can, and move it centimeter by centimeter. With the squat, we accomplish this by doing a box squat, so there’s no stretch reflex/rebound. For the good morning, we do this by suspending the bar with chains. For the bench, we can do this with pause benching, rack lockouts, etc.
But when it comes to the press, think about straining in that movement. It’s REALLY hard to do. Typically, when a trainee starts straining in the press overhead, the back starts bending to compensate, strength gets leaked all over the place, and we don’t really get a chance to strain in a productive manner, if at all.
Here I am trying to do exactly that
It’s hot garbage, and that’s my BEST straining effort on a press overhead.
If I were REALLY set out to want to do it, I’d do seated back supported presses overhead with various lockouts, but those will quickly turn into VERY high incline benching instead.
It’s where I find the conjugate approach lacking when it comes to pressing overhead specifically. That said, I think pressing is pressing, so I’d be totally fine with horizontal style pressing as the max effort work and then using your dynamic effort work to drill the overhead. RE would work there too. But with a bench press/variant, you have something solid to drive your back into to make a base to press from and can focus on total maximal strain.