I am very glad to say that my problem has been sold with the newest release of pie-register. The Username and Password field label are now editable. Woo-hooo! And I have noticed that a great deal of new strings have also been added to .po file. Many thanks to the devs!
One set of labels I still did not find in the .po file appears in the form users see after they click on the %reset_password_url% link in the reset-password e-mail. The missing labels are “New password”, “Confirm new password” and the submit button “Reset password”.
I guess, you are all too busy for an answer, I hope you at least have time to read through. Please, continue the great work and thank you very much for the fix again!