Just mentioning… I don’t know exactly what the “Forwarding Across Context”-option is for, because I don’t have this one. I just thought it would be worth a try…
Also in my MODX-manager (which is set to german language), when I open the “babelLanguageLinks”-TV, there is a sentence stated in the descriptions-box meaning something like this:
“This gets managed through the Babel-plugin. Please don’t change”
So I guess you shouldn’t do any changes in here. So I would “reset” your changes and don’t give access to some particular templates, i would uncheck all templates (which basically means that this TV has access to all templates - if i am not wrong).