The problem here is the Windows registry. Firefox Portable doesn't properly read the registry where the location of Native Messaging script file is defined. This would need a change to the Firefox Portable that it would allow to read Firefox registry entries outside the portable application. The only solution for this could be to use PortableApps Launcher and tweak the registry settings from there. See https://portableapps.com/manuals/PortableApps.comLauncher/topics/registry.html

EDIT: The issue #1817 is updated with the latest findings. Please continue the conversation there is possible.