When I first saw this post, thought about all the prohibitions that would be involved.
Perhaps there is a way to wash it without being oiver on any Biblical prohibitions or on any major Rabbinic prohibitions? After all , in some situations dishes can be washed on Shabbos. Waxing would have to be skipped. Have warm water from before Yom Kippur on a “blech” for both washing and rinsing. Use only the right kind of brushes, not cloth. Of course the car would have to be in a proper eruv and far away from any grass. Pre-mix the soap in the warm water.
Did I miss anything?