My solution was not what you're asking for, but maybe you can at least get an idea? I h ave the same type of shelf unit, I think, wire framed? I split it into 2 shelves plus the top. You could mount the LEDs I am talking about to the bottom of the shelf, but hanging gives them more versatility (closer when young, lift when taller plants are growing?)
What I did was buy 2 of the cheapest LED lights. Only red and blue. No infrared, no UV. This suits me as I have found no definitive answer whether or not orchids need those, and I have fabric art work in the house that I don't want exposed to those wavelengths. My room was always good for those things, as it has no direct windows, and it had space for the shelf :P So far so good except for this cold snap we're having!
So this lamp is cheap, it's bright in it's spectrum (won't look as bright as a white light) and has been working. It's lightweight (featherweight) and seems bright
Cons:
VERY flimsy feeling (hey but works!) not waterproof, no cover over the LEDs no timer
to me, no timer is a good thing though. Most timers only turn on a set number of hours. I use
a smart plug and I can turn it on and off when the sun goes up and down (dawn to dusk) thus giving the light the same hours of sunlight we actually get outside (seasons automatic) Of course you can also set the hours you want. I'm totally addicted to these lights. I have arthritis, so discovering someone left the lights on in the back of the house, I can just say "Alexa, turn off desk lamp" and it's done :P
Well, that's the cheapest route I've found. My shelves are 3 feet wide, about 2.5' to 3' tall and I use 2 per shelf. Also, I split the smart plug up using
a multi plug thingy. Anyway, hope this helps you get an idea of a possible set up as cheap as I could do it :P