There were two ways: to enlarge the diameter of the gear (but so I'd have also to build a longer brace between tripod and motor), or to try to make much little teeth on the same diameter. Second choice should have been impossible to make by hand, but with a laser cutter perspex plate it has become reality (thanks to Waldy which helped me).
Step 1: Laser cutter absolutely needed!
I attach the dxf file with all three cogs so that you can see or utilize it to make something similar.
Step 2: The transparent gears
Step 3: The metal handy connection
You see how the metal locking bolt pipe remains in the socket I've created in the inner circumference. There is a thin black rubber band between the tripod head and the gear, so it's tightly steady.
Step 4: Dismounting the motor unit
The issue is that the little nail which push the teeth has to make a shorter route because the teeth are much smaller, so closer each other than before.
On the same time I want to keep the chance to use any of my three gear sets, so I've decided to add a nail behind th exeisting one.
So let's take the motor gear apart.