I'm tiling my upstairs bathroom and would like to use a marble threshold underneath my door.

I've read a lot of different ideas on how to install it, mostly being on top of backer board. Problem is if I install it over backer board you will be able to see the profile of the backer board, thin set when its all finished. I have wood flooring upstairs that continues into my bathroom, so I will be building up the floor in my bathroom causing that issue.

Has anyone tried a white liquid nails type product and glued it directly to the wood? is this feasible if I liberally cover both wood and marble surfaces and let it dry for a week?

I've also thought about cutting into the wood floor, the exact size of the marble threshold, I would then put 1/4" backer board into the spot I cut out and install the marble on top of that.

Any other ideas, please let me know