The reservation system has always been a bit sketchy in my mind as the reservations are run by the landowner. One year, I called at the opening time of 7 am, got ahold of them at 7:02 and all the reservations were taken. Other years, the phone just rings and rings and nobody answers.
The one time I did get a reservation, the owner was not happy that I couldn't show up a week in advance to pick up the reservation slip.
I would try, but focus more effort on the ones that don't require reservations.