Thread: Replacing Internal Stairs

I am thinking about replacing an internal set of stairs that connects the 2 main levels of our split level house (1.86m height difference). The main reason is that they are getting old and are fairly basic (not even rounded at the nose), made from pacific maple; and I'd like to increase the riser height and tread depth slightly by reducing from 11 steps to 10 (giving a 186mm rise and a 245mm going / 275mm tread). I plan on using a good quality hardwood for the risers and treads. I will also add a skirting to each side of the stairs rather than just butting the gyprock walls as it does now.
In order to minimise any demolition/rework necessary, I plan to simply add two new stringers (360x45 LVL possibly) inside the old stringers (cutting off all the steps on the old stringer in-situ).

Now for my first question: There are only two stringers on the original stairs (which are 930mm wide and were built with the house in 1985), but I have read that the recommendation is to have three stringers for this width. I have never experienced any flex with the existing stairs (treads are 30mm thick and risers are 20mm thick) and do not want to add unnecessary expense and difficulty to the project. My thoughts are that the hardwood will be much stronger than the maple, each tread is fully supported along its length by the riser underneath and the riser at the back going up (by screws through the riser into the back of the tread). Also, the new stringers will slightly closer spaced (approx 790 centres). Is this reasonable?

My second question: I note from youtube tutorials that the stringers are usually screwed into deep joists on the upper floor; however in my case the joists are 90x42 hardwood and run parallel to the stringers. The builder has skew nailed a cross member between two joists (there are double joists each side of the stairs to support the walls each side), but the stringers are not butted against this cross member. The top ends of the stringers appear to be mainly supported by some steel strapping nailed into the joists and the stringers beneath them. Is this OK? It seems a bit suspect to me, so I plan to physically butt them onto the cross member and screws through to the stringers (as well as screwing them to the old stringers which are strapped to the joists).