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Nice article.
Rather than use two batteries in series and lose power with the 1k, it might be better to use just one battery with a lower value resistor like 150 ohms or wire the two batteries in parallel rather than series, that way battery life will be doubled and you won't waste power at the resistor. I'd suggest using a small potentiometer in series for brightness.
Any details on how to cut the perspex?
Will grinding the inner ring provide uniform illumination?
If the led's aren't going to stay on continuously, you could even use button cells in parallel although the holder will be a challenge.
Will give this a try
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