Solution: Personalize an incentive gift.
In your invitation, state that if they register by a certain date, that they can expect you to present them with a special gift with their name on it. Whether or not you choose to share what the gift is or the value is less significant than making them feel like a V.I.P.
You can decide to prepare the same gifts for everyone and only those responding early receive ones personalized OR simply keep that gift as a thank-you for helping you with your numbers.
Personalized gifts that are relevant to the individual and the event will be put to immediate use and kept long after the event is over.
And what if you prepare gifts with names of people who don’t show? What a great opportunity for you to follow up with them afterwards, offer to deliver (or courier) the gift with some event material. What a great way to ensure everyone participated at some level.