Hi Bob, thanks for your comment. I really appreciate it and it makes sense other than my nosing doesn't stick out at all. This is the nosing that will be used:

Does that change anything?

Nosing should stick out per code and because it feels more natural when walking up the steps. Is there a door here?

There is no door, just a cased 4' opening

I would find that a trip/fall hazard. Normally the floor should have the top step flush with the bottom door frame. Even in a basement, the floor juts out a short distance from under the door before the next step down.

As long as there isn't a door swinging over the steps, I don't think that setup is a hazard. However, I would include a handrail, even if one is not required.

Thanks for the input everyone. The stairs are 12 inches deep so I'm not too worried about having the nose overhang. I think the code says no overhang is needed for stairs over 10 inches deep.

I wasn't even considering a hand rail but it's probably a good idea.

I still think that since your instinct is to not expect an immediate step down when going through a doorway that it would be a hazard. Look around your house and see how the steps are spaced and you'll see what I mean.

Assuming you're the owner, reasonably skilled and only three or four steps are involved, why not tear them out and replace them with exactly what you want?

Run the nosing on the threshold to the side walls. Let the casing die into it.

Thanks everyone. This is what I ended up doing. I appreciate your input.