Any periodization scheme works only as well as the choices you make for your assistance exercises, especially with a lift as complex as the push press (it's much more technique than it seems). You need perfect body position during the dip/drive phase and good timing between the leg drive and arms.
A lot of people make the biggest mistake in the dip and drive. They so a short "knee jerk"... basically just bending at the knees, the knees travel forward as do the hips (so the hips are directly under the shoulders) this gives a very weak drive and the tendency to push forward.
Look at the dip position: lower back is arched, the dip is controlled and while the chest stays up the hips move back slightly. Then the drive is straight up.
Good assistance exercises include not only shoulder work but also movements working on the dip and drive phase, like half front squat (focusing on perfect body positions) and half push press (driving the bar just above the head).