Hardwood options in large master bath

[sleepy hollow]

Wet hardwood floor is slippery

It can be.  Tile is the same.  The coefficient of friction for many popular bathroom tiles is not good (i.e., low), BTW.  Hardwood, like tile, that has texture, like brushed matte sheens, will have a higher COF.  Nevertheless, water is an excellent lubricant and care should always be taken in wet floors no matter what the composition.  Also non-slip rugs can help.  I would expect to have one or more rugs in this room even if only to attentuate sound.  

A fully tiled or hardwood floor will also tend to be loud without some sound dampening on the floor and walls.

[sleepy hollow]

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I was wondering how long it would take for this post to appear. ...

This is a great discussion, and I very much appreciate the advice and opininos.  

One thing that occurs to me is that you all may not appreciate how large and tall this room is for a bathroom.  Most bathrooms just are not like this one and so it is hard to imagine why anything else but tile would be appropriate.  Maybe I am wrong, but I invite you to look at the measurements in the drawing and imagine a 12 foot cathedral ceiling besides.  Its is a small barn.  It has five rooms in it (counting the shower). 

As for using cement board, I tend to use Schluter products and have used their DITRA menbranes on several projects elsewhere in the house, including on this same level when I expanded and remodeled the children's/guest bath down the hall.  Frankly, I cannot recall, but when I researched it many years ago, I am pretty sure cement board was for flatness and water stability, not structure.  But I could be wrong.  I studied all the TCA specs and standards and, at the time, only DITRA met the specs for tile to substrate decoupling needed to handle the flex.  

Anyway, I honestly and sincerely appreciate all the thoughts and discussion points provided and fro the time you all have taken to express them.    

We have a lot to think about and consider as we review the approach to the flooring.