I know that if the GTW event has registrants before you connect it to your program, you can't connect it, but I'm not sure if you can connect it if it has no registrants, but your program does.
If not, you can create a new program, connect it to your GTW webinar. Then select the 1,600 members of your program and change their program status to registered in the other program. Then you can abandon your current program and use the new one.
When you registered the 1,600 members, did you send them an email with a link that would enable them to join the webinar? If so, you'll likely need to resend it as each registrant gets a unique ID assigned to them from GTW when they register for the webinar and your prior email would not have had that.