Embed your Google Form within your website and let it slide out when needed. Super lightweight. No backend needed.
All necessary CSS and JS files are in the respective folders. An HTML snippet for the feedback is provided in index.html. Copy and paste that into your code to add it into your website. Make sure you replace the necessary information that identifies your Google form. To gather the information, go to your form's page and inspect the HTML. Look for a form HTML tag -- match it up to the entries in index.html to complete the process.
Runs on JQuery. Bootstrap is used for button styling, but not needed.
Live demo here: https://dl.dropboxusercontent.com/u/113142954/dropbox.html