I went ahead and tested it, and while the regular hits do deal their appropriate damage, there is a definite issue with Critical Hits when using Ki Damage.
This first screenshot shows a Regular Crit for my character.

Notice the physical component of it. 138 Physical damage.
Looking at all the flat added damage 27 + 4 + 1 + 2 + 9 = 43 Physical damage.
Multiply by 3 on a crit and it's 129 minimum Physical damage, just from the flat added damage alone.
Now compare that to the second screenshot, which shows a Ki Damage Crit for my character.

Notice the physical component of that one. 107 Physical damage.
The flat added damage is still the same: 43 Physical damage.
The multiplier is still x3, so the minimum Physical damage should still be 129, but it's not.
It's 22 lower than the minimum.
At first I thought it was Northlander Hewing (+9), which was buggy, but even discounting that in the numbers it still doesn't add up.
27 + 4 + 1 + 2 = 34 flat Physical damage. Multiply by and the minimum is 102.
So far so good. But Ki Damage maximises all Physical damage rolls, so at 1d6 that would be 6, multiply by 3 = 18.
The total Physical damage should then be 120, but it's not. It's still lower, sitting at 107.
Something is not right with the way Ki Damage calculates damage on Critical Hits.