Uchitachi's men cut is a cut that they put everything into. Uchidachi’s intent is not to cut down to gedan level, but to cut down to the navel. Since the cut misses shitachi, it goes all the way down. Uchitachi should not lower the body or lean forward much.
Uchitachi should not pause or hesitate to strike men. While there is a slight pause, don’t stop and wait for irimi, as soon as you feel shitachi moves a little forward then strike. In the Kendo Kata Manual published by All Japan Kendo Federation, it is said, "Uchitachi executes a men cut at a moment when shitachi is going to get into irimi".
Of course, this is a kata and you have to have good timing. You don't want to go too fast but you have to know the theory.
Shitachi’s kensen is at the level of Uchitachi’s face in chūdan hanmi. After irimi, shitachi should move more forward than sideways. There should be just enough sideways movement to move the body off of Uchitachi’s line of attack. Mainly the movement should be forward to get into position to strike men.
Shitachi should hold the kodachi with a slightly relaxed and flexible grip during ukenagashi. Too loose though and when shitachi deflects uchitachi’s men strike the kodachi will get knocked back into shitachi’s head.
Ukenagashi is a deflection that directs the incoming strike just slightly off center, towards the left. It is not a block. Shidachi’s right hand should be above the head with the kodachi pointing down to the left with the blade toward him.
The deflection and follow-up men strike should be one smooth motion but shitachi should complete the strike before transitioning to jodan and exerting zanshin.