Seriously, this has to be an "inside job", meaning an ex-member, a barred pilot, someone turned down for membership?  They know too much about what rutting does to a field, about the cameras and their locations, how to remotely enter the property, and when to do their antics.
Take pictures and or plaster castings of the tire prints.  Get your officers in a quiet meeting and see who might have reason to do direct damage to your field.  
Setting out ANY deterent that causes harm/damage will end you up in an expensive law suit and whether you win lose or draw, the attorney fees will eat your money up.  There might be game wardens, utility surveyers, adjoining livestock that are harmed by spikes.  Granted they shouldn't be out there at night but it all boils down to the "what if" scenario.
Put out additional night cameras and don't publicize that effort or location.  You'll catch them on camera and that's all you'll need to go to the police with.  This might be an active member but kids with their Daddy bought 4 wheelers and do donuts anywhere.  They don't specifically target airstrips unless there is some specific vengence in mind.