LZ7-04M2PD appears to be the closest thing to a substitute (please share if there are others) but does not have a compatible pin-out (see below). It might be possible to control some of the LEDs and insulate the pins with incorrect polarity. Ideally though, the component would be substituted with a different LED.
Harrison- have you given any more thought to hosting the project files?
LZ7-04M100:
Pin Color Polarity
2 Red +
3 Green +
5 Blue +
6 Amber –
8 White +
9 Cyan –
11 Violet +
14 Violet –
15 Cyan +
17 White –
20 Amber +
21 Blue –
23 Green –
24 Red –
LZ7-04M2PD:
Pin Color Polarity
2 Red +
3 Blue +
5 Green +
6 Lime +
8 Lime +
9 Amber +
11 Cyan –
14 Cyan +
15 Amber –
17 Lime –
20 Lime –
21 Green –
23 Blue –
24 Red –