I have fully resolved my issues with my Mac Studio not remembering which monitor is which. As my previous post stated, I am using a CKLau KVM Switch, and this switch has built-in EDID emulation.
The EDID Emulation appears to trick macOS into thinking that the monitors are still physically connected and turned on, even when I am not connected to the active port the Mac is on. I have tested this extensively with putting the Mac Studio to sleep and waking it up the next day, and even fully shutting down and starting up.
Not once did I have to rebuild my desktops (triple 2k monitors), or had any icons move, or have any monitors not waking up. I am getting a full, Triple 2K/1440 @ 144Hz picture and performance with zero issues.
Originally I had an issue with my monitors turning off and on as I said in my previous post, but it wasn't the KVM's fault, it turns out that the three different brands of adapters and cables I tried out all had the exact same issue with supporting a stable signal. When I tried a much cheaper fourth brand of USB-C to HDMI Cables, it solved my issue and now I have a Mac Studio that acts like a normal computer for once.
The good news: I no longer have to rebuild my work environment whenever I wake up my Mac. All monitors will turn on and stay on. All icons remain in place. I don't have to leave my Mac Studio on indefinitely any more. And no more headaches.
The bad news: In order to make my Mac Studio function like a normal computer with multi-monitor support, I had to spend an extra ~$500 on a new KVM Switch, with new USB-C to HDMI Cables just so the Mac will not forget which monitor is which. Another Apple Premium I had to pay.
It took 10 years for me to dial up a KVM/cable combo solution just so my Mac acts normal.
I suppose whatever this KVM Switch is doing, maybe someone can find a cheaper method to keep the Mac tricked, and perhaps finally get some peace. It's clear that EDID Emulation helps with this, at least via HDMI.
For Reference, this is the combo I have that works 100% with my Mac Studio M1 Max solving the "which monitor is which" issue:
CKLau KVM with EDID Emulation: https://smile.amazon.com/dp/B07RSV2WZP
USB-C to HDMI Cables: https://smile.amazon.com/dp/B085HC43Q9