Hi everybody! Back to this topic to tell the news.
I paused this project for some time to do easier work on other clocks – and make some money 
Then I came back to it. Well, here are the pics of the things put together on the lathe (1st version):
The first and second attempts to cut the contrate wheel failed. This structure was not good enough to hold the blank.
In the first attempt the teeth were not cut at the same height, so I added a screw under the blank holder to keep it in place.
In the second attempt the teeth were not cut with the same width. The blank holder was too tall and was side moving with the lathe vibration and the cutter strokes. So I added a second wood layer to hold it closer to the cutter, this way:
Third attempt… I was tired, these days are very HOT (summer here) temperature about 30°C. Repetitive work and discomfortable body position causing some pain in my neck and arms…
-position the blank
-lathe on
-sloooowwwwlyyy feed the blank trough cutter
-lathe off
-return blank and move to next tooth
-lathe on…..
After almost two hours… – TADAAAA!!! Perfect!
Next pic shows the cut wheel after cleaning, removing burrs and polishment:
I still need to cut it out of brass rod and install in the arbor. But even after this I won’t be able to test it because the escape wheel has a broken pivot. This is another subject I will leave to someone else to do because it is an extremely thin pivot – about 0.1mm!