Bathroom Floor (Mud Bed) Removal and New Floor
Not sure I understand, Are you saying the joist had the top 4" removed?
Just does not make sense to me, how big are the joist?
Then again, it did hold 4" of concrete so should be stout.
I like the idea of sistering them for a few reasons. which would mean removing the 1x6.
Leaving the 1x6 could cause weird squeaks, simply cant do anything good for you.
So pull em out and get them out of the way, I would try to be careful, could be some nice tight grain 100 year old wood you can use on another project.
I would want to use 2x8 to sister the joist, give you enough meat to screw them solid, I also use liquid nails on them to help eliminate squeaks.
Now you want to determine the finished floor hight to the hallway, or whatever room you enter while exiting the bathroom, to get a flush or as close to flush as you can get.
No tall threshold to trip on.
All you need for sub floor is 3/4", go to the big box store, it will look like osb and will be tongue and groove. Is specifically made for sub floor and has the engineered strength.
I would use hardibacker on top of it, you have a choice if 1/4" or 1/2", the 1/4" is good if you have flat surface, since yours will all be new, 1/4" would be fine.
Then the thickness of your tile adding for the thinset under it, is the finished floor hight of your new floor.
This is why the sistering idea is good, you now know how high to set that joist, you can raise or lower it to where you need it. Then you use a level to set the other end.
I really would be surprised if your 100 year old house floors were still level.
By sistering you get level and correct floor hight., and is worth it to me.
I hear a lot of talk about ditra, I did a quick google search for it the other day to see what it was.
Looks like a membrane that I use when building shower pans, do not understand why it would be used on floors, I should read more on it.
I do know that simple hardibacker will work for what you are doing. But is your choice.
I would not mind hearing more about why some choose ditra and what conditions they decide to use it.