Even if they give you the same rate, the Events and Meetings group would make you sign a contract. And that contract binds you as it doesn't allow for cancellations. So you are probably better off using the online tool as they suggested. I have done that before with over 20 rooms.

And as has been suggested, instead of putting your Marriott number in all the reservations, find 3 others who have Marriott numbers and put their number in. Remember you will only get points for up to three rooms. So basically, 3 people can get points for 3 rooms and one person can get points for 1 room.