That trim makes no sense on that wall take it off and leave it alone.

Whatever the right layout of trim is, it's not what you have now. (How did that happen? Why the needless cuts?) It shouldn't be this hard. The original red sketch line was better, but actually should have been angled somewhat higher to match the overall slope of the stairs.

Yeah, that's not good. Sorry. Where the stairs go down, the rail should go down at the same angle, and when you have a landing, the rail should be level.

I have kind of a funny story about wainscoting on a stair. I have a 1910 duplex, and the stair to the upper unit has a rail, with embossed wallpaper below. The wallpaper is gorgeous, but...when they applied the wallpaper, they basically unrolled the paper down the angle of the stair. The wallpaper has medallions that are all at a slightly wonky angle because the stairs aren't 45 degrees. I rather studiously avoided figuring out how much off of vertical they were, and tried to pretend it was just an optical illusion. It only bothered me occasionally, and not so much that I ever wanted to get rid of the otherwise fabulous wallpaper.

Does that handrail feel natural as you walk up the stairs? Your stairs don't seen to have an even pitch, so the rail might be exactly right, but you should make sure.

Wainscoting with a rail should match the rail angles. Unfortunately, your handrail has some crazy angles, which makes me feel like you should forget about wainscoting here.

This is what you would want wainscoting with a handrail to look like.

Since they are winders the rail could follow the stair skirt exactly.

Many houses here have box winders and the rail is curved and metal or they forego an outer rail and have one or a couple vertical rails on the inside of the radius.

I set the handrail on my winders by the height of the treads at the corners.

Palimpsest - Yes, I think that's what we're going to do, follow the stair skirt exactly.
Thanks all, glad I wasn't alone in thinking this was crazy (the contractor is still defending his plan - apparently he doesn't see what we all do, but is at least willing to take it off and redo to match the skirt instead). Going to check it tomorrow and help him with the boxes - we're drawing these with pencil first :-)

He projected up 90 degrees from each change in angle it looks like, which canted everything forward and distorted some of it. By following the skirt, he will be projecting straight up from the horizontal plane at each change in angle so it should follow the skirt exactly and be in the same proportions. He meant well.

You need to hire a finish carpenter who specializes in staircases.....asap......go to a stair store, and go see the workmans jobs......but yes I agree with advice given....molding sooo expensive, you need someone who measures twice and cuts once....

He is trying to follow the line of the kick board but messed up a bit. It needs to match better or your wainscoting will be off. First, second and third board down that are way off.

Without being able to see the plane of the walls clearly, I can't criticize his work.

We were going to have him do our fireplace surround to the ceiling - glad we tried him on this first - will now find somebody with more woodwork experience for the next project. Thanks.