OK, so how about something like the below then?
Part 1: Hardware-side
Part 2: Software-side
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With the SEL_SdCard pin held LOW (active), I can write to the SdCard, then once done, pull the SEL_SdCard pin HIGH.
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Then, with the SEL_74HC595 pin held LOW, I can write to the 74HC595 registers, then bring SEL_74HC595 pin HIGH. The chosen LEDs now turn ON or OFF as was instructed (/written to the registers), and are maintained that way (until the shift-register is communicated with again).
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And then continue by starting again with the SdCard when necessary, then the 74HC595, and so on.