Have you considered a VIP pass where you pay a higher monthly membership fee, but don't pay seat charge? Maybe even cut the queue when there's a waiting list.
To qualify, you need x amount of hours in a month. Similar to frequent flyer / loyalty programs. That would encourage players to frequent the place while also ensuring the games are running. First playing lots to qualify, then to profit from it as a VIP. Kinda like shills but with their own bankroll.
There would of course have to be a limited number of VIP memberships available and you would probably have to gift the first couple of months to the current regs to get it going. Then others will pick up on them not paying seat charge and want to get in on it as well. Maybe make the players show the VIP card when seat charge is collected to make sure everyone sees it.
VIPs that don't meet the required monthly hours would be relegated and has to work themselves up to qualify again. Be open about the program so it doesn't seem unattainable for the semi-regs. "Hey Joe! 11 more hours this month and you qualify for the VIP-pass!". Eventually you might even get a waiting list on the VIP pass and at that point you'll be all