Without seeing it, I don't know that your mechanical assessment is accurate. It probably has more to do with your lockout position and your traps than it does your triceps.
My current bench is 210x3 and press is 150x3 (I know I am weak but that is fine for I am working on it). In the overhead press I can lift 165 off the shoulders (say up to the eye level) but my triceps aren't strong enough to extend my elbow to lockout in the standing position. On the other hand they have no problem locking 210 in the lying position.
What is the mechanical difference of triceps involvement in presses?
Without seeing it, I don't know that your mechanical assessment is accurate. It probably has more to do with your lockout position and your traps than it does your triceps.
Could it be cause by tight latissimus dorsi?
Dunno. But they are not terribly difficult to stretch.
I will be going on a little vacation and I will post a video of my OHP once I come back.
So I guess if I get my traps stronger I will see quick gains in the OHP and please correct me if I am wrong.
Primarily, you need to learn how to use them.
Wen I press, I always unrack, pause on my upper pecs and start the press with a quick shrug motion while i lean back slightly and push. Doing presses with the pre-lean as described on the book just doesn't work for me. Of all of the exercises, presses are my fav. (and cleans just because of the amount of effort i put into getting form down, then 1 day, "got it"). Using the "shrug" to propel the start of the press, I've worked up to a double at 165 and a 202 "self taught" single jerk. If only I had a set of traps to assist on my squat.....
To clarify, at the start of the press, I use my lats to drive my shoulders down, while slightly leaning back storing elastic energy in my traps, then without pause, I use the energy stored in my traps to begin the process of "launching" the bar upward. From there, All I know on heavy pressing is that I try to use my entire body to channel energy and motion to the bar and at lock out, I feel my traps squeezing like a MOFO. Doing the press this way assures that my triceps are never the limiting factor. now, talk about the bench and tri's can limit me all day long.