Finally fixed the problem with my JGecko U file. It was simply due to the location of the actual JGecko U file on my computer it seems, which is kinda weird. It NEEDS to be in my User's default Downloads folder for it to work properly - if I move it anywhere else it'll spit those errors back out at me, even if it's on the same drive. Also, this isn't a problem with my firewall and/or antivirus, as I've already added exceptions.
Whether or not I get the JGecko U file manually or just get it from running the Gecko U Updater, moving the file to "C:/Users/<Username>/Downloads" makes it work. Is there any explanation to this?