To remove soap from glass shower doors, use baby oil and a scrubbing sponge. After, use a glass cleaner to remove the baby oil.
Voila, no more dried up soap on your shower door!
Your idea of cleaning the glass shower door is a good one. This is what I did when we had a new bathroom in an addition. Our shower in the new bath is large 3X5 and was built large intentionally as we had a handicapped adult to be showered. As I had to help him with the shower we put a curtain on a spring rod inside the shower so that I could pull the curtain partway while helping him and keep from getting wet myself. I discovered shortly that the curtain also kept the water away from the glass door. Now we still pull the curtain while showering and the glass never gets soapy water. When the curtain needs washing it is a simple matter to just put it in the wash.