Lifting Program focus on OHP?

I bruised my tailbone a couple years ago and all I could do was OHP for a few weeks so I did Smolov Jr and just plugged in my OHP numbers. My max went from 110 to 120 (strict press) in 3 weeks which wasn't too shabby. You could start out with something like that while doing a standard lower body routine then switch to a full body strongman routine. I think Kalle Beck has a free one one startingstrongman.com, and they have monthly training templates for fairly cheap. Depending on where you're going you might be able to find some strongman gyms along the way for implement training.

I use 5/3/1 for OHP. I can't remember what the recommended accessories are specifically...

I started with pl coach to increase bench. As accessory to bench, she had me hit shoulders. She put me on the front delt press machine, lateral raise machine (don't know exact names of machines, but you get the idea), db lateral raises, rear delt crossovers, rear delt rows (all 3x8). My OHP shot up...went from PR of 60lbs to 80lbs in a few months (after being stuck for several months).

If you just want to go for strength, I'd recommend the Waterbury 10x3 method which allows you to use heavier weights for just 3 reps but still achieve hypertrophy by doing 10 reps. If you start to go really heavy 8x3 should be suffient to still achieve hypertrohpy because 24 combined reps is generally considered the min # of reps necessary to do so.

I use this method for the 4 main compound lifts, including OHP, and have consistently achieved increased strength by means of linear progression using an increasingly higher estimated 1RM target
goal.

When doing OHP or other lifts, I'd suggest using lower increment increases limited to 1-2% especially if you are doing the lifts more frequently than 1x a week and/or incorporating very short rest periods between sets because of the increased level of difficulty.

In order to find more info on the method, just Google the "Waterbury Method" and "10x3." Good luck!