Is there a way to say "I respectfully thank you" to familiar elders?
You could say 谢谢您 instead.
When you really want to be super respectful, especially to some respected person who you are not quite familar with, you could go with the following

承蒙关照，不胜感激。
厚情盛意，应接不遑，切谢切谢
感荷高情，非言语所能鸣谢

There are many more here which you can check out.