Wanted to update the thread in case anyone was interested. I received a replacement fuse (Side note: I think similar fuses can be found here:
https://www.digikey.com/en/products...4kYYACx0UIdJGz5iZSiACscBgDU2nHpH7Cxk6XMUrlyoA BUT I'm not sure, I didn't get this specific one but it's ratings match the one I got.)
Installed fuse after removing the old one and reviewed the Audio and GPU flex. Did a bit more soldering to ENSURE the best joins my eyes could see using magnification.
It worked! Powered the PS1 up with HDMI and got output/solid LED. Buttoned up the rest of the unit and ran an EA game (Need For Speed Hot Pursuit 3) and got ALL HEARTS!
Really happy with this outcome. I'd like to thank everyone for the assistance in this thread, much appreciated! XStation will be my next addition once those ship out.