Is there a way to use the Only allow one response per person (requires login)'

No, that is not supported. Only forms which can be accessed via a URL, public or private, are supported by the plugin. The way the plugin works is your web server actually handles the interaction. With Google via the WordPress HTTP API. I think the only way to do what you want is to embed the form with an iframe.

You could require logins to your site and control access to the form that way. It would still be possible to submit multiple responses but you could prefill a hidden field with the username.