Can I move a joist a few inches left without the ceiling falling on my head?
Those joists carry dead/live loads of the closet floor, any walls resting on it and that transfer loads, foot of any attic stairs etc.. There is also a load transferring from the studs you mention via a bottom plate (not visible) onto the joists.
If you remove the joists during work, you have to support the flooring and bottom plate that rests on the joists.
You also have to check what's loading the double rim joist there. What exactely is resting on it?
Even if the load is minimal, supporting the joists will also prevent any temporary deformation that could crack your wall finishings or separate fastened members.
Work on one joist at a time, while supporting the others.
Building a support is easier than you think. If the load is entirely on the perimeter of the space above, you don't have to support the flooring itself (between the existing joists), but you still have to support the bottom plate on which the aforementioned studs are resting.
With support along the perimeter of the space you can remove the joists, cut them, and re-insert them. Again, it's important to check what's loading the double rim joist that shall be move back: stair stringers, wall studs, just flooring etc...?
To provide support you could use two or three vertical 2x6 or 2x4 over the width of the stair case, resting on a flat 2x4/2x6 pressing up against another flat 2x4/2x6. You can cut the verticals slightly over-length (by 1/8&quot;) and jam them in until they provide support. Or get a 20ton bottle jack lift.