I see nothing wrong with doing doing overheads as a max effort movement, but must realize that you are supposed to rotate every 2 weeks. You are going to need bench. You don't necessarily need a spotter. You can set the pins in the power rack to various heights. This would sort of be like doing board presses. Also, I don't like your reasoning. If you are weak at something then you should address it not ignore it. This is the one of the most fundamentally principles of westside training.
Hey Pemdas, you are spot on. My problem with benching is mostly in the lower rep range, and only with barbells.
It's not a weakness per se, rather, I think I have an imbalance of sorts which makes for some bad right delt pain.. I worked on form for a while, no dice. for this reason, I've been doing mostly dumbbell benching and unilateral benching (dumbbells, but one arm at a time) on previous programs Also a lot of rowing.
If I manage to remedy this problem, I'd love to improve my bench press. I hate excuses, so slap me if I sound like I'm making them.
I am doing the same thing right now. Push press and strict press are staples of my ME work, boards and rack lockouts as well because I have trouble locking it out. Pushing stuff over your head is cock diesel.
I work out at a powerlifting gym. I tend to look at the form bigger guys use, which might be the problem. I don't tuck in my elbow (not until recently) I tend to bring the bar down on my middle/lower chest.
As far as the imbalance, my left side doesn't activate well on its own, but I'm pretty vigilant and it is improving. Strength wise it is similar. The pain is also worse if I do inclines, it's as if something is clicking with my right shoulder in every rep.
I think there is an injury there because whenever I do sprints or any intense cardio I feel a pain on that same spot on my right shoulder/delt as my heart really pumps. I have booked an appointment with a physio and still waiting for it (health service isn't great for sports injuries)
This injury did not happen in the weight room, but it could be a result of some sort of training mistake before I found T-Nation.
That's about all the relevant info I can think of.
Not to play internet doctor/sports trainer, but it sounds like you have an impingement. Stay away from OH pressing, unless you use a neutral grip, and benching all the way down to your chest (use board presses instead). You'll also probably want to do some rotator cuff/scapular rehab/prehab movements to make the area stronger and more stable.