Finishing with 안녕히 계십시오 or 주말 잘 보내세요 sounds extremely stilted and formal to me when they are just saying '안녕!' to me. How can I show respect and still sound friendly and cheerful when saying goodbye? Or should I just worry less and try to sound more natural when using respectful endings?
Adding to @JSong's great answer, you can add "또 전화 드릴께요 (I will call you again)" as 'good bye':
안녕히 계세요. 또 전화 드릴께요.
Or you can add "건강 조심하시고 (Literally, be careful with your health. Take good care of yourself)" before "안녕히 계세요":
건강 조심하시고 안녕히 계세요.
If you are calling them on Thursday or Friday, "주말 잘 보내세요" is another great alternative.
"안녕히 계십시오" doesn't sound friendly.