maybe by removing the pull-Hi resistor off the HC165 Circuit, and using a Inverter on its inputs
for example:
https://www.mouser.at/ProductDetail/Nexperia/74HCT1G14GW-Q100H?qs=SKY61BOKKY4Uv%2FaFLc8SsQ%3D%3D
https://www.mouser.at/datasheet/2/916/74HC_HCT1G14_Q100-2937184.pdf
(just a example maybe there are better parts for this porpuse, and i dont know how hard to solder this one is)
that would reverse Lo and Hi, and you could use this bloddy 3 LEDs ( where i think thats not a good idea, the Encoder is expensive - and not really a standard part...)
but for that quick idea i would prototype that first (order a inverter, order a Encoder, make wires without pcb) ... specially iff any pull hi or pull low resistors are needet elsewhere, i guess you need a 10K pull-low resistor (to ground) on pin 3 off your Encoder then:
HC165 > Inverter > Pull-Low + Pin3
since i have not much time these times, and you have plenty off modules what module i should check next?
i just had a look on your 4x2 Enc RGB SW Led ring Rgb render here... and i am not 100% sure that the inbuilt RGB LEDs that enlighten the Encodersshaft dont shine on the LED-Ring and make them hard too read (maybe need some lightshielding)... by the way hard too read, those Alps Knobs are a bit big for that small Ledring - can you still see the LEDs when looking from a angle that is not 100% from top?