Then you're basically screwed. You have got to figure out a way to pre-soak the car down. Some car washes have a pre-soak option on the dial but the amount of soap it puts out usually sucks. Maybe you could use that soap brush and let the thick suds DRIP all over the car (whatever you do, don't allow that brush to touch your paint). You're in a pickle.
As for spreading wax, I use a black pad and my PC. I don't spread it by hand but I remove it by hand. I explain what towel I use to remove my wax in the videos.
"Marines - Making the other guy die for his country for over 200 years."