I just thought of a typical make up table in a dressing room that I have improvised numberous times.
The ones I have helped to throw together with various community theatre companies out of sundry backsatge storage rooms to create 'proper' make up stations.
We make the back board about 3-feet wide, put a string of 3 screw shells each side of the mirror, and one along the top, and then run a short return of about 6-8" out from the backboard on each side to separate one make up staion from the next. Actually this frame also helps to stabilise the vertical rear backframe. Ppaint the whole thing with white paint, to make the chip board look a little more pleasant, and then also improve the diffusion of the lights. Stick half of a back of bedroom door plastic mirror in the middle of the backboard at a slight down angle so the person can get a good view of face and hair while seated.
Screw in 7 60w old fashioned incandescant lights and everyone is happy. Good diffuse lighting.
So for this project I just threw things together kinda the same way - no mirror, two lights where the mirror would go, and then fiddled with the screw shell spacing while temporarily fitted with 25w incandescant footlight bulbs for visible output.
I stuck my integrating dome refective light meter at a constant height over the edge of the box while it was inverted and played with distance from the side wall, and distance between lamps while the screw shells were held in place temporarily with masking tape to see what gave the most uniform output. Then I screwed them into place.
The lights ended up further from the side wall than I thought they would- I guess a lot of the side output of all of the lamps bounces off the side wall more than I expected. Turning them sideways may have put more light out, but it would have been heaps more of a PIA. I presumed that UV would be refelcted the same way that vsible was, and so far this presumption appears to have held true. I tried with aluminum foil on the top behind the bulbs agiast the socket tops, but it gave me worse uniformity.
Good luck with this project.