Use the GitHub API to determine repository validity.

We were previously attempting to access GitHub repositories directly
through Git, which required a valid SSH key configured. This led to
some problems.

1. It required that the user properly create and associate an SSH key.
   While annoying, this was actually made worse by the "Associate SSH
   key" checkbox, which associated as a deploy key. Deploy keys could
   only be used for one repository at a time, and this caused massive
   confusion.

2. It meant that we only knew that a repository could be accessed by
   that key, but we didn't know if anything else was invalid.

3. It was a problem in networks that didn't allow SSH access to the
   outside world.

4. When validation failed, we didn't know much, and the resulting error
   was hard to figure out.

Now, the GitHub API is used to validate repositories. We can tell the
user that the repository wasn't found, and list possible reasons why. We
can also make sure that there isn't a mismatch between the selected plan
and the public/private setting of the repository.