I have both a colorized version and a black and white version of this for the very reason you stated. I don't remember posting the pic above, but I have that, too. Haha.You may not be completely happy with the final appearance of this LED design. If you really want to put this much effort into such a project, you should start with a bit of lighting design/effect "research".
First, some modern LEDs are extremely bright and become blinding at 20mA as @Yaakov suggests so you should connect a small group and test them at currents down to 1 to 5 mA range (less blinding). At 1mA , your power supply can be a very manageable 2 amps instead of 40 amps as yaakov feared.
next, you should build a small section of a stripe. You may (likely?) find that your rows of rows design does not suffficently distribute night. LEDs are point sources and intense. They will not look like a red stripe. You may have much better effect by distributing your red LEDs in the whole area of the red stripe. Looking at your design without the red or blue infill will give a better approximation of the final result. Finally, you may want to look into light diffusing films or resins. You can fire the LEDs sideways into a light diffusing resin (hot glue or casting polymer with some TiO2 blended in.
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