Our strength levels on the overhead press are currently about the same. I've always struggled with it, but recently have started seeing some steady progress. There are some differences from cleaning the bar first and lifting out of the rack:
- The clean catch position is a bit wider than out of the rack.
- A clean catch is better suited to finishing with a push press or jerk rather than a strict press.
- Balance can greatly affect the amount of force you need to produce.
I've found that for me, the following technique points have helped me perform better with the strict press:
- Use a false grip. The bar should be sitting across the palm with the thumb outside the bar. I find it helps transfer power better; but I do need to use wrist wraps to support the grip.
- Initiate the lift with the lats. This provides the force to get the bar off my shoulders to about eye level.
- Get under the bar as soon as possible. With the bar over the crown of my head, I have better leverages to lock out the lift--and it consumes less energy.
These are all things you can do directly out of the rack. With the second bullet point, it should take care of what cleaning is supposed to do before you press. One thing you do want to be careful of is that cleaning the bar first does require a lot of energy. If you do enough sets, you run the risk of fatiguing more quickly.
You may need to work on work capacity rather than strength. Work capacity training takes what you can do for 3x5 (about 70%) and expands it to 5x8 or something along those lines. The first three weeks you would increase one rep per set, and the next couple weeks you would add a new set. After you give yourself a little rest, you should be able to drop the volume and increase the weight over the next few weeks until you hit a new PR or two. My coach usually works this into my training at different stages, and I find it really does help. The added reps also really help you fine tune your technique.
In general, I find I really have to increase the volume on this lift to get it stronger. There's a number of strongmen (like Kalle Beck and Bryan Hildebrand) who also echo this sentiment. In one of the American Strongman Radio webcasts, Hildebrand would work up to a top set As Many Reps As Possible (AMRAP), and as he took weight off the bar he would keep doing AMRAP sets until it was just the bar. By the time it was there, he was so fatigued he could only get around maybe 12 reps. It can't be done every training session, but the massive volume day really helped keep driving his press up more than anything else.
NOTE: in strongman you have to clean whatever implement in any way you can during competition. Many strongman do train a clean to get the bar in position and then press for reps. However, just as many also train the press separately. They also train both a strict press and a push press/jerk. The push press would be used for competition, but the strict press is there to build strength throughout the lift.