I train almost entirely on instinct, no set plans, reps, % etc.
What I have noticed though is I tend to rotate through focusing on one aspect with the other as secondary. Whether I do pushpress first and military following. or warmup with military and when the weight gets too heavy start push pressing.
My biggest gains came from working on my C&J. explosiveness is the key to a big PP. IMO
Never entirely strict press. I feel like I'm limiting myself if I do. My chest day I do incline bench probably 50% of the time that would be about the limits of my strict press. I'll usually finish with strict DB OHpressing. I'm far from being the best OH presser but I've come a long way. First attempt at strongman I manged to just get over a 200# log. Just this week, I missed 295 at lockout.