I don't think the GBA screen can be lit from behind.
I found the website
Portable Monopoly, where they're working on this.
The original idea was to replace the screen, but that would be too expensive.
Then they figured on lighting from the edges, but the existing screens don't reflect from such low angles.
Now the guy is looking into a special reflection system that bounces low-angle light straight down onto the screen. Depending on the cost, that'll probably be the best solution.