I know this is an old thread, but I faced the same issue: surface mounted medicine cabinet 4 7/8" deep. I found a Kohler Tone 3-light vanity fixture Model #31770-SCO3- BNL (brushed nickel one) that was perfect. It extends 10 3/4 inch out, but it's only 6 inches high. It was beautiful, but after ordering from Lowe's, it went from delivery 6/12 to delayed to out of stock. Damnitall. Whoever reads this...it will be available in October, 2023. I talked to a Lamps Plus clerk who said the entire bulb must fully extend out past the medicine cabinet to avoid all shadow. This Kohler model does that. I had to totally switch gears to a fixture that pointed up. I hope it will work to provide enough light. I'm not as thrilled about it, but you have to be practical to get the bathroom remodeled in time. I hope this is helpful. Good luck to all who face this issue!

Dreaming, oh, I thought I needed a bathroom fridge for my cold cream. :) And it probably doesn't cost much. Babka, yesterday at the glass/mirror shop they told me that if I wanted a framed mirror to get the frame first and then they'd do the rest. I need to go back and get some idea of prices. You're right, I could get a decent frame. I could also get a frame that matches my vanity, although I'm not sure I need to match it, just coordinate with it which is more my speed. I don't see what's so wrong with a little vertical storage at eye level. Do you put your hydrogen peroxide and Pepto Bismol in a drawer? Don't you just see bottle caps and have to lift it up to see what it is? The medicine cabinet I have now in the photo is horrible faux wood crap. It might find a home in my garage, but not even the mirror is worthy. may_flowers, Mirror Mate looks pretty cool and isn't too expensive. I'm not keeping my existing mirror. My vanity is just 30" high, so with a new one at 36" and making sure the lights don't overhang the mirror, I need to get something smaller, at least not as high. It might end up that a new mirror and frame will work out better. I wouldn't have a recessed cabinet in the side wall if it didn't have a mirror. It may be that electrical in there would need to be moved in order to recess so that's something to consider. I'm not sure I love the look of a magnifying mirror on an extendable arm. I don't really need a magnifying mirror.

I see that you will have 2236 lumens with that fixture. It might not be enough. I have 2 fixtures at about 1600 lumens each (3200 total) and it is a little dull. I think it may be due to the thick-ish frosted shade. I have another bathroom with 2250 lumens and it seems to be better lighting. Different fixtures though, and both of mine are halogen. But Lumens are lumens I believe. If you are in doubt would you be able to use 2 fixtures and put them on either side of the cabinet? You could put it on a dimmer too. I really think your vanity/sink is a cute setup.

I'd cross post this in the Kitchen forum for some ideas on layout. You have a lot of space to work with. A larger version of your plan with readable measurements or individual sections will help. 450 footcandles at the counter for work surfaces is good to shoot for. Under cabinet lights can help. You have a lot of pendants over that slim island. Those Liteline fixtures are used in RVs and boats where there isn't any space above the ceiling. But they do put out light at up to 600 lumens for 9w. If you want to see them in action visit an RV dealer. A 5th wheel like a Montana or Jayco Pinnacle will also give you a feel for a slim island. For ambient light you can use 6" recessed IC fixtures and regular A19 bulb configuration leds. These are maybe $4ea in dimmable at Costco. They use 15w and produce 1100 lumens in a flood pattern that lights up a large area.