I don't get it, you've got a website people go to on a regular basis and you collect contact info. Why not just throw up a giant box after users log-in saying:

I don't get it, you've got a website people go to on a regular basis and you collect contact info. Why not just throw up a giant box after users log-in saying: "Hey $user, you've been an active user of our site since $signup_date and we'd love to hear what you think about how we're doing and what we could be doing better?" Add buttons for "Sure", "I'm busy right now, but ask me later!" and "No thanks" and call it day. People love to give their opinions on things. They'll go out of their way to do it. Look at how many people (myself included) are doing it right here in this thread. It takes minimal effort to get people talking (and even less to get them complaining). If you've got enough users people will even do it themselves. They'll create entire forums and subreddits just to discuss your product/service all on their own. It might not be a bad idea to set up a space for that kind of thing yourself. Discord is a good place to start.