Question Is there any way to do this? (wiring & logic gates)

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Terrarian
I basically say this title sarcastically as what I am doing is neither easy nor having an obvious solution.

I came to forums exclusively for this question for the time being and I have got thus far without assistance, but now arriving at this problem this is my last free resort.

I am creating a menu select for a game inside terraria. My problem is that there is no way to combine the data of shift registers into a larger one with only 4 colors of wire. I need to use teleporters and because of the nature of the mechanism being all parts adjacent to each other, it just can't happen realistically. I am using 8, 5 number shift registers that are unidirectional and need to combine them to one because there is no way to set an off value efficiently for each one without the very mechanism that they are supposed to work for and the very same I need now.
I know I am very vague, but I have world files and screenshots of the machines if needed. I don't want to explain this whole thing if it is a simple fix. I am very ambitious so if someone asks don't be surprised.
I will check in on this page but probably somewhat infrequently, because school.
 
I just made this image, I know it isn't accurate
2025_05_11_0f2_Kleki.png
 
(Update)
I have created copies of these shift registers outside the mess of wires to make them easier to access.
 
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