I used a different email address for the employee but that doesn't resolve the issue.  There is still no way for her to select the template on the Invoice creation screen because the "Customize" button is not available.

However I did figure out a (somewhat clunky) workaround:  By going into Settings, then Manage Forms, she can make the template she wants to use the Default.  The only problem is that she has to do that 3+ step process every time she wants to use a different Template.