Preciseness and precision

Fowler says to avoid -ion words to describe a state or quality and to instead choose -ness words for this purpose. -ion should describe a process or action.

Yet he writes:

So far as the words are used with overlapping meanings, preciseness is differentiated by implying the importance of precision is exaggerated. Preciseness rather than precision is the attribute of a precisian.

So what does this mean? Merriam-Webster also seems to say that preciseness carries "so strong implication of severity or strictness", and gives an example as "there was a certain amount of preciseness about the young man".

What do you think is the best choice? By ear, I was just going to replace preciseness with precision.

Precisian has at least two senses:

• A religious purist; a Puritan.
• Someone who strictly observes the rules; a pedant or stickler.

Also, besides the sense "The condition of being precise; precision", preciseness also has a now-dated sense, "pedantic behaviour". It is apparently that sense of preciseness, and the second sense of precisian, which Fowler is concerned about. That is, by "Preciseness rather than precision is the attribute of a precisian", he meant "Pedantic behaviour, not precision, is the attribute of a pedant or stickler (a precisian)". While Fowler's remark is correct, most people aren't concerned about what a precisian is, so the distinction that Fowler pointed out is of minimal relevance.