Ideas for using a closed stair

There's no such thing as US building codes, there are state, county, and municipal codes which vary widely between areas. The only way to know is to ask, which is what I'd recommend you do. There's no harm in it, simply call the office that is responsible and ask. You don't have to say you've already done it if you're worried about it, you could say you are planning on doing some remodeling and ask them if a door opens into a landing if that's OK and see what they say. Worst case is you have to turn it back in the way it was.

There are 2 ways to do this, the first way is in essence just cutting the wall at the top of the skirt board and capping it off and setting the handrail on top of the cap that is finishing off the cut wall, sounds a bit crude, but essentially that describes what you will have.

The up side to this is you will not need to do a floor repair, depending on where your wall ends where the newel will be.

The other way to do it is by removing the wall entirely, repairing the floor, removing the treads and risers, and set longer ones with return nosings on either side. and re-support the stairs with a new walls under the existing carriages.

This is the most work, but will give the best result in my opinion.

Jan. 2, 2014 edit

Here is the work I did in 1989 that shows what I did. This one shows the best example of the effect I was trying to explain. I do not have a shot that shows how the handrail goes past the ceiling, but with a little imagination you could picture what the rail would have to do if the stairs were much wider at the bottom.

Edit #2

I did a little calculating to help, if it may