This should add the flathub remote to the system and then install all the existing user packages into the system level. Then removes all the user level packages.
flatpak --system remote-add --if-not-exists flathub https://flathub.org/repo/flathub.flatpakrepo
flatpak --system install $(flatpak list --columns=application)
flatpak --user remove $(flatpak list --columns=application)
Personally I would just pick all the ones you’d like to be global (system level) and leave the rest at the user level.
I’ve had installations hang a long while before eventually succeeding. I would also ensure Windows has hibernate turned off and quick boot disabled.