U want to bring ur super infantry against my super monks? We'll see who gets Castle first and this Unique tech will finally bring over hordes of archers too.
Apart from light cavalry, the weakness of monks is to sheer numbers, especially when those numbers are cheap. In the same way that Aztec monks can't keep converting against an imperial age Gothic infantry flood, the monks you propose wouldn't be able to convert cost efficiently against cheap infantry, especially if that infantry is the woad raider on steroids. Mind you, if you do want to make a monk civilisation, I would borrow the Turkish gold mining bonus, as you'll need a lot of gold for monk production.
Unique Tech: Logistica (Monks have chance to convert extra units)
This is straying outside the bounds of the problem. Logistica is a trample damage technology. In order to make a dream civilisation, we have to stick to technologies as they actually exist. None of the unique technologies in Age of Conquerors are applicable to monks, but the Slavic unique technology from Forgotten Empires would be suitable (Orthodoxy - monks +3/+3 armour).