I like getting custom PCBs made at places like OSHPark. I would try to make a design where I could use flat PCBs joined along the edges. You can get flexible PCBs for not much more cost but that's going to be too flexible. Maybe a thin PCB material can be flexed and staked out to the required shape? The cost of all that square inches is going to be expensive no matter what PCB material you get.
The example shown looks like polycarbonate drilled/cut on a CNC machine and then possibly hand-formed to the required shape. The back of that is going to be a complex thing with LEDs wired to each other and to off-board wires. Lots of opportunities for screwups. I'd still consider placing flat PCBs behind that.