I'd say it's unlikely you're going to find a sheet solution to that which will be cost effective, unless money really is no issue. I'd go with LED strips, or hand wire a solution.
Yes, wired it by hand. Didn't take all that long... but yours will.
Variation in lighting is actually a laser engraved paint mask on the back layer. Overall illumination is VERY consistent.
LED strips would be more cost effective than a sheeted solution. Bagged by the thousand LEDs will be even cheaper than strips, but I'd recommend making base panels of laser cut acrylic to plug the LEDs into, perhaps 12" panels at a time. Bend over the legs and solder. Given a piece of 20% white translucent, or some frosted P95 matte clear and 1/4" air gap, this will provide a very even illumination.
Another option would be to do an edge lit panel with super bright strips, and a CNC cut grid pattern to diffuse the light upward. Or, make edge lighting with 100% density by hand wiring LEDs. Like this: