From your description, the only remotely cost-effective way to ensure only paying shooters can use the course is to enlist technology. There'll be a significant investment up front, of course.
One way (not the only one, just one that came to me immediately) would be to use a vending machine to issue an RFID bracelet or tag with payment, then have targets activated by reading the RFID. This will require a computer to control the targets, actuators for each target (to rise up or move into view), RFID readers at each shooting station, and wiring the course to connect everything (or installing wireless equipment, likely somewhat cheaper to install and much cheaper to maintain). For safety and tracking, you could also use RFID activated gates to enter and leave the course -- activation of the exit gate would replace the sign out list now in use. As a safety bonus, the computer could include a function to notify someone (the course operators or rescue authorities) if a shooter doesn't leave the course in some reasonable time longer than the normal time to walk and shoot the course -- and, of course, once the RFID has been used to exit the course, the managing computer would disallow that same RFID tag from using the course again (though if desired, the course management could also issue "season tickets" or "lifetime memberships" that are issued from special blocks of RFID tags).
Of course, this depends on having a fence around the course, but you need that anyway, for safety of non-shooters.
Once the initial investment is paid, maintenance costs will almost certainly be much less than paying a wage to a gate guard, and you can likely increase the course fee for the "pop-up targets" -- targets could, for instance, be on a delay after the RFID is read, could "run" or "walk" across an opening in cover, etc., which would be attractive for sport shooters.