So can you make the first page of the survey a request for an email address, which you send a verification email to. They enter their email address, you send them an email with some sort of uid in the url, they then click that link to continue with the survey.

Obviously, you'd need to log the email address to make sure you only send one email to each address, but that should be the only thing you'd need to keep a record of.

This would seem to provide enough verification of individuals, without too much assing about on the end user side.