Saving node with a text format another user doesn't have permission for renders it inaccessible
You can't I'm afraid.

Think about it like this: When rendering the text to screen, Drupal has to decide which text format to use to filter it. This means that per field, there must only be one text format, regardless of which users have edited it.

If this wasn't the case, Drupal would have no idea which format to use to render the text. It would have to guess, which is something you don't want a computer doing!

If you want users to be able to edit textarea fields, your admins will simply have to save them in a format that those users have permissions to use. Otherwise the whole point of having different filters available for different roles is kind of lost.

But the main point is that conceptually, if different users edit the same field, with different text formats, then Drupal has no idea which one to use when outputting the field value. This is why you cannot do it.