OK I got it. Like so many that come here you want help but are unwilling to give the group the tools needed to help you. This after all is All About Circuits, not Look Into A Chrystal Ball.@shortbus questions have no relation with the problem that is Controlled linear motion with 3 position stages, 10% tolerance is acceptable, speed is important, ~20ms would be great, force of ~5N
You want and need to stop and think about how a solenoid atually works. Small is harder that you think. In the electric solenoid or actuator world things of the size you want don't exist. You have to accept some things in life and the physics of electromagnetism is one of them.
I asked about some things that are how changes and improvements are made in engineering and it has insulted you, I guess. Well good luck going anywhere and getting help when you can't or won't state the problems up front.
I won't waste any more of your time or mine.