You could build shelves in a stairwell https://www.pinterest.com/pin/528891549974717015/ around each window and door frame and around the top of the wall of each room above window height next to the ceiling. http://topotushka.com/marvelous-interior-and-exterior-designs-on-ceiling-bookshelf/ceiling-bookshelf-unique-on-interior-and-exterior-designs-intended-for-bookcases-ceilings-reading-nooks-spaces-8/ https://www.pinterest.com/pin/329396160216860642/ https://www.pinterest.com/pin/276619602084864857/

"Because the shelves and walls behind them weren't configured for LED strip lighting, so significant reworking would be required, i.e. running power in the walls to the shelves and modifying the shelves to accommodate the lighting?" I'm not sure how familiar you are with low voltage LED tape that you configure yourself (I'm not talking about ready made fixtures) but if you're not, it might be worth a look. It's not as complicated, time consuming, difficult, or require the modifications you might think. In fact it's kind of fun to design and install. You'd only be running one line voltage drop - same as you will be necessary to the ceiling. This is a good website to learn more about all the possibilities and options: https://www.ledsupply.com/ Just another option to consider.

Start by removing everything, including what's behind the doors, giving the cabinet a good cleaning and inspection to see if it needs to be painted or repaired. Consider changing the hardware for a lighter, beachy look. Think about using luan or foam core to cut inserts for the back of the openings, so you can paint or paper them and change the vibe at will. Sort photos, decor and books into labeled boxes or categorized piles/stacks. Then reduce the items in the categories again, separating the sentimental items from the generic ones. Next, go to the sentimental categories and work through them. What is important about this item, was it a gift that means something, what is it that attaches you to the item, does it really need to be displayed or is it just a special keepsake? The items that you must keep, but don't need to look at or display daily, can be kept behind the doors. Work through the generic items in a similar way. For me, I would first decide how hard it is to keep the item clean. In my case, the topiary, the basket and the birdcage would have to go because they're intricate and are hard to clean dust-catchers. This may be a good time to analyze items in the rest of the home. Some may need to be used in this cabinet (or not.) Anyway, spring cleaning is good for the soul. When you put the cabinet back together use 1/3 books, 1/3 large decor and 1/3 open space. Don't line up items like soldiers, but layer them. Photos can be used but should be in different sizes so you can layer them for interest; trios of a large one behind two smaller ones is good. Don't put photo groupings on the same level of shelf, but mix them up, still keeping them low enough to be seen, and limit them to two or three groupings. Books can stand, lean or stack to support other decor items. You can wrap books in other paper to change their look. Decor should be large enough to be identified from the seating without having to approach the cabinet. Small photos will be better if put on tables in the room for closer inspection. Keep the top clear until you've staged the rest. One large item might be sufficient. You can also light the shelves with LEDs it you think that helps draw the eye to the shelves instead of the top.

I think it will look fine if it was a narrow built in and placement of books is attractive, so it‘s visually appealing. If you have a lot of books, there really isn't going to be a lot of space though. If your main goal is to make the space more appealing, search staircase landings on Pinterest, but I think a nice window treatment would do wonders The paint color is really dark and a soft, light color will not only brighten the staircase but make space feel larger and the windows less prominent. Not a small job to paint, but would make a big difference.