You need to find re-dried PT lumber for the kind of stair you are proposing. The problem that almost nobody addresses is that the tread cuts change shape (to a sloping curve) when they dry after being cut wet. Because the material shrinks as it dries and what was once a straight line is now a slight curve, So your costly ipe slab treads are not going to be sitting on a flat surface.
You could make the stringers from 14" PT parallam beams. These have already been re-dried and have the strength you need for a very long stringer such as you propose with such a great dead load (weight of the Ipe treads) With that material you could confidently build the housed, notched stringers. Make the notches blind so the treads slide in from behind, and it will look nicer.
Casey

if you dont let PT sit for a year and dry.it will go crazy.
or buy pre dried as said.any wet PT that sits FLAT will twist/crack badly from rain/sun.

I have a similar project going on as yours. My stringers are 14ft in length and I'm using 3/4" thick ipe for treads. If you sister your notched stringer to the inside of your solid outer stringer, the gap will probably turn into a debris and moisture trap causing your stringers to cup.

Since my treads are 3/4' thick I had to use middle stringers. To make them stronger I decided to set them lower than the outer solid stringers so I wouldn't have to notch them as deeply. If after completion it vibrates too much to my liking I'll install a couple 4x4 posts at midspan.

My existing staircase has a center stringer setback from outer ones. From your description, I would recommend against notching outer stringers and either put a 2x4 block under each step stringer connection(step screw down into block, block nailed into stringer) or use Simpson tie angle bracket or equivalent to connect step to stringer. At longer lengths a notched stringer is very weak. 4x4 posts will help, but a solid stringer is better. I believe stringers cupping can be prevented by using dried wood and sealing it on installation, but would like to hear any feedback on this issue. Two stringers sistered present a relatively thick beam. My biggest fear is curve in vertical direction. Using bolts through both beams to hold railing posts adds further strength(Although I am limited in bolt options due to 2.5" Aluminum posts with Al railing being used.) Wish I could find wrap around brackets for railing which would allow thicker bolts...