Just popping with a little extra. If anyone was in the same situation as I was where Win7 would not allow me to install ME1 off the disc to the x86 directory:
On a hunch after bryaco identified the missing files I threw my disc in and tried again. Originally I was going to install it in a different spot and copy/paste the files over but this time it recognized my Origin install and let me overwrite it! Once I had the UNC files in their place all I had to do was update through Origin and everything was finally good to go, smooth sailing now.
I sincerely hope for all of you who don't have original hard copies that this gets sorted out as quickly as possible, I always have and always will consider the Mass Effect franchise to be one of the very best I've ever played and that's saying a lot when you consider I had a game controller in my hands when I was 3 and I'm 37 now 😉.
If there was a definitively legal way I could post the folder for you all I would. If for some reason Origin is having a hard time finding them since they're almost a decade old and are probably archived somewhere you have my e-mail address! Lemme know if I can help!