edit_posts capability now works fine, possibly because we did not network-activate

Yes, it could be the result of single site activation as plugin does not get the full set of options, which it has when it is activated network wide. I need to know what the problem you met.
For example, if you activated ‘edit restrictions’ add-on, then you need to check ‘create_posts’, ‘create_pages’ capabilities in your administrator role, in case they are not included there automatically.