I'm not sure you need to make reservations.
Obviously there is a need for reservations from some people going to the campground, or they would not be doing implementing that system.
When I want to go to a government park (COE is my most common type of federal park) - I look at the recreation.gov web site and look at open sites at the park for my size unit and needs. If it looks like less than 10% of the campsites are open - I will call the campground/ ranger station and ask about usage.
I might make a reservation 5 days or so before arrival. I'll usually reserve for 2 or 3 days.
For campgrounds not busy - I just show up.
I've never had any problem extending my stay - if the site was not reserved by someone else - out to the maximum permitted for that campground. When I arrive and ask for a site - I always ask if the individual site is reserved for any period in the next two weeks. I try to get a site which is open for two weeks. That can change over night - so be aware.
I have no idea about the usage percentage for the Chaco campground. Outside of holidays like Memorial Day, Fourth of July and Labor Day weekends - I would not expect the campground to be full / booked.
I'm hoping to be there either in mid-May or late September/ early October 2014. I'll find out if I'm completely wrong about the usage.