The biggest barrier to effectively progressing any variation of DB presses is the inconsistency of getting into the starting position. Whether it's flat, incline or overhead presses, having to fight with the weights before even beginning the set is not a recipe for success.
The key to mastering the "kick back" is to find the perfect balance of energy expenditure and stability, but this is often easier said than done. In a classic example of "success breeds more problems," increasing strength and advancement within the press just means bigger, heavier and more cumbersome DBs.
Is there any way that we can reliably approach this problem in our journey from 10s all the way to the 200s?
The most effective approach can be simplified to:
Incline of Overhead Press -> Stick with the "1-2-Press" technique
Flat or Decline -> Utilize the "Roll" method
Let's first break down the "1-2-Press":
1) The DBs should be further down the thighs near the knees. This will allow you to get more power into the "kick" as well as afford some clearance for the DB to move from leg to shoulder.
2) Starting with your dominant side, use your hip flexors and biceps/forearms/anterior delts to pop the DB up to the bottom position of the press. Take care to judge the effort required for this because you don't want to come up short or sail it too far (both could potentially be injurious).
3) This is the most important part...LET THE FIRST DB SETTLE! Don't try to move to the other side while you're still attempting to stabilize the initial kick. Find that base first.
4) Once you have full control, repeat step two with the weaker side.
5) Now that both DBs are stable in the bottom position, you can press to lockout!
Now onto the "Roll":
1) Start with the DBs high up on your thighs, closer to your hips. The larger the DBs, the closer they will need to be in order to create stability.
2) Make sure your body is facing directly in line with the bench. You definitely would not want to blindly attempt this and completely miss (speaking from experience).
3) As a unit, rock your body back. Keep your hips flexed at 90º in order to control the DBs.
4) Ideally, you would want to be able to "catch" the DBs close to your lockout position as your back settled into the bench. This requires a good amount of coordination, stability and strength, so most people will find more comfort in controlling the DBs on the chest until a stable base is created.
5) Then you can press if you didn't catch the DBs in lockout!
As you can see, there is a good amount of complexity and moving parts in both of these techniques. It will require a lot of practice to solidify the timing and get confident performing both variations with heavier loads. It's OK if it feels awkward and uncomfortable the first few times; the key is to be able to save energy and reduce risk when you need it most later on.
Lastly, I want to mention the importance of a spotter when it comes to DB presses. Failing a DB press is much safer than its barbell equivalent, but I've seen too many instances of people getting hurt before ever even starting the set! When possible, have someone you trust (and ideally someone who can easily handle the load you're using) stand behind you and "guide" your path into the initial lockout. This will drastically reduce the instances of injury and also generally allow you to get more volume in or handle more load than you otherwise would have been able to. Never underestimate the effectiveness of a good spotter!