I gather your "indicator" matrix which behaves itself perfectly, is connected in parallel to the same power and control lines
For either of these solutions the output stage of the MAX7219 drive would have to be rewritten.
I would consider just trying it out in daylight with your current arrangement, with the brightness register in the MAX7219 set to maximum.
In other words, you would not be using the MAX7219 but instead, a series of cascaded TPIC6C595s (or 6s) for which the code is somewhat simpler - but different - to the MAX7219; you have to reload all of the TPIC6C595s at once whereas the MAX7219s can (I am not sure what code you were using; I gather it was a library) are actually updated one column at a time.
This is certainly the way to use high voltage LED devices - of course you are back to using one wire to each individual LED plus a common. A "12 V LED" is in fact three LEDs in series with a resistor but as 1W LEDs necessarily draw 350 mA, you may require the higher-current version of the drivers.