You can even make this clear in the "leave Earth in a fast ship and return" scenario - have the people on Earth send you a birthday card by radio every year tha

You can even make this clear in the "leave Earth in a fast ship and return" scenario - have the people on Earth send you a birthday card by radio every year that you're away, on your birthday in their reference frame. You'll receive those ticks of time as you travel (most of them on your way back).