going down the scale produces this quite marvellous result
20.61818181818r /100 x 99 = 20.412 this is the imperial equivalent of your base 100 sacred unit.
20.412 / 12 = 1.701 this is one step from Thom's base unit
20.4 is the unit scaled down to 1.7
This is a side length of 3022.22222r and the unit of translation is 10/9 and this converts to 2720
So the system works perfectly and produces the base unit discovered by Thom.