My Buddy that is not a member but always has something to say to me about this stuff just emailed me questioning why I didn't explain what should have been done for this opening.
To start with may I say, "we don't know what we don't know" and "we only think we know what we think we know" and then there is a little bit that "we do know"
What we do know.
2x6s spanning 13 ft are at their limit for supporting a ceiling, they will carry much more weight but there is a sag issue.
As they land on the walls just below the knee walls we can assume that they are load bearing walls and we did our best to prove that with what looked like good results.
The problem is the wall three feet away that is now supporting the cut floor joists. all the weight from this part of the floor is transferred to the floor below which could cause a sagging issue in that floor.
Anything we do to repair this, the weight some how wants to be transferred to the foundation. An engineer might calculate the weight and how it might disperse thru the structure but I can only go on what they all call for in new construction and renos that I have worked on.
Normally around a staircase like this would be to hang the cut floor joists from a double floor joist which is hung off a double or more at each end.
The problem with this fix it that as it is just 2x6s there still could be a sag, which would then just put the weight back on the non bearing wall and the floor below.
Now we could put bigger beams in but then they would protrude thru the ceiling below. Probably not a good option and then we would also have to open walls all the way to the basement to add more studs.
If I was standing with an engineer I would make suggestions based on what he wants to to do and what would be easiest for me to do.
My suggestion would be to just address the sag in the floor below and that would be to go one floor below that pull the ceiling and double the floor joists or maybe every other floor joist under that area. I think an engineer would go for that.