If you said to me "Do as you would be done," the first thing I would have to work out is how I "would be done", how I like to be done, how I like other people to do me.
That has no meaning relevant to this context.
"Do as you would be done by" is an old expression that is always seen in that form. "To do by" means to treat someone a certain way, usually in the expectation that the treatment is reciprocal. Just Googling the phrase, I found:
Confucius said it in reverse: Don't do what you don't want someone to do to you. Here is the Wikipedia version.
Perhaps his most famous teaching was the Golden Rule stated in the negative form, often called the silver rule: 子貢問曰、有一言、而可以終身行之者乎。子曰、其恕乎、己所 不欲、勿施於人。Adept Kung asked: "Is there any one word that could guide a person throughout life?"
The Master replied: "How about 'shu': never impose on others what you would not choose for yourself?" Analects XV.24, tr. David Hinton