It seems a strange place for a light fixture, on the underside of the upstairs bridge. Both the stair and the room opposite have double height and should have chandelier fixtures, though I can see the stairs has sconces over the landings. It's not what you asked for, but I would want to minimize its visibility by replacing it with a fixture that blends in as below.

Pot light in upstairs area and only hang chandelier in the stairwell.

I love how you added the door in many colors to our house, Beth H. You are all making me wonder if I'd be better with a rich navy instead of a turquoise front door. Both Kensington Blue and Indi go-go are pretty similar. Do you all like the navy better than turquoise? Any other ideas? Thanks!

Pagenie, I know this is a late response, and maybe you've already made your choice; but maybe it'll help someone else. I don't have long enough experience with my clip-on LED lights to tell you they're going to do the trick for you, but I think they're worth considering. I had to go with this as opposed to any overhead-suspended fixture because my plants are in my living space, and I can't do anything industrial looking here. Built-in timer (3, 6, and 12 hr options), long "bulbs" on goosenecks, adjustable brightness. I got two, one for either end of my four-foot near-window space, because where I live - well north - the daylight hours get very very short in winter, and not only that, but November is a notoriously gloomy month. Clouds, rain, snow. Anyway, here's what I got. https://www.amazon.com/gp/product/B07ZHTNFZ6/ref=ppx_yo_dt_b_search_asin_title?ie=UTF8&psc=1 I like that the light from it is not purple, pink, or blue, but a nice clear white that seems to enhance the colors of my flowers and doesn't make me think "plant light" when I see it from across the room. These can also be used as a work light for people who are into handwork like embroidery, tatting, knitting. Unfortunately they've bumped the price up $7 per fixture in the last month! Oh dear... Joan