We flew into Jacksonville in May, 2002 and used National. We are EC members and always use EA when it is available, so I had a similar concern. We were pleasantly surprised on arrival to see a sign at the National desk inside the airport directing EC members with reservations to bypass the counter and go directly to the garage. They do not have the large number of EA cars like at MCO, but they had a line up of full size (which I had reserved) and midsize ready to go. As I approached the National area, an attendant asked me for my reservation confirmation, asked me which car I wanted, took the confirmation and my EC card, drivers license, etc, went into the booth to process paperwork while I loaded the car. He returned in about 2 minutes and we were soon on our way. It did not take any longer than my experience using EA at MCO.
BTW, National and Alamo had already combined operations at the Jacksonville airport at that time, so the booth (really a small portable office enclosure) had both National and Alamo signs. The cars were in different aisles of the garage, however.
Ralph