My friends dont spend so much time leaving water around like that!
Yes the 20 minutes issue is worth while for the Chlorine!
What you should do is boil up your water in a couple of saucepans till its bubbling. Pour this hot water into you distiller and set it away. This will knock at least an hour off the time. I do this because my distiller is old and I need to preserve as much as possible plus the energy saving of course as 1 hour of my 500w unit is 1/2 unit of electricity.