The issue has been escalated to our developers. The problem stems from the fact that those jobs that can't be reviewed are private CPTs that can't even be previewed in the default language.
As a workaround, you can edit the original language layout and use the language switcher in the toolbar to change to the translations and directly publish them from the back end. Or you can approve translations using the bulk action "Approve translation reviews" in WPML > Translations.
We will keep you updated on any news regarding this issue.
I will have a try at your suggested workarounds as I need to keep this project moving forward. I will revert here with my progress or any issues I encounter.