If you make the argument that a private company, by shutting down a user's account, is like government restriction on free speech, then how do you determine the balance between the right of free speech and the right of free association?

Remember, freedom of speech is only one part of the First Amendment. Those same writers also included the freedom of association. An organization like Google, Fox News, Amazon, or the Wall Street Journal is not obligated to associate with everyone.

We can change things. We can pass laws which mandate that certain things are public spaces. For example, the rise of the malls means that the migration from public shopping streets to private shopping areas, where mall owners like the Mall of the Americas can shut down protest much more readily than the police could do in a truly public area. We can pass laws which force malls to be public areas. The Supreme Court decided that in Pruneyard v. Robins. But only a handful of states have done so.

We can similarly pass laws which say that any content hosting site must be content neutral. Eg, if you want to use Stack Overflow to post your diatribes against whale hunting, SO cannot shut you down.

That doesn't make sense. Okay, so we only require that of "powerful" sites, which you suggest. Which is defined as .... what? Who gets to decide? Who gets to challenge that? If Yahoo was once powerful but is no longer so, who gets to decide when the transition occurs?

One possibility is to set up a common carrier status, where a company offers its services without discrimination to the general public. This is how the phone system works. But why would a company want to do this?