Permissions - How can I keep my permissions as-is but allow for a specific field to be visible?

Unfortunately, a snapshot field of a look up field seems to behave to respect the permissions of the look up field so that won't work. But we can kind of build our own snapshot. I suggest you make a text field called like [Employee name.] Which has a similar name to the real. [Employee name] field and then use both a form rule, (and I would back that up with a pipeline) that says when the record is saved and the [Employee name.] is not equal to the value in [Employee name], then change the value of [Employee name.] to the value in the field [employee name].

You can initialize that frozen field by doing another look up of the employee name and then change the field type from being a look up field to just a text field. That's a quick way to populate all your existing records.