It may help if a chain is put across the access points from the pits to the runway.  Also put the remains of damaged pit stands in the tall grass around those access points.  That would prevent people from going around.

A chain at a reasonable height would allow most planes to roll under on the way to the runway.  Also pilots could step over it to retrieve a plane.  ATVs and other motorised vehicles would not be able to drive through. 

The other option is to NOT cut the grass at the 2 ends of the field fence.  Then only put a chain across the opening in the middle of the fence.  Once the grass grows a bit at the ends, put tree branches, remains of broken pit stands, and other obstacles in the grass. 

If there is a combination lock and a keyed lock on the chain, members could have access to one or the other means of opening the chain.  It is highly unlikely that asking someone to keep out will be enough. 

Asking a good neighbour to observe could put that neighbour and their property at risk.  The same hooligans will visit that person's property.  It may pit one member of the community against another.  The local people already know who is doing the damage.   They are just reluctant to do or say anything.

The flying field is almost totally surrounded by corn.  Every portion of the field in corn is important to the landowner.  The access is mostly by the laneway.  From the pictures in post 1, the tire marks heading to the field appear to be mostly through the openings in the fence.   Picture 3 shows that grass or wild shrubs are pretty much surrounding the field.   From other posts of the field taken by drones it seems that corn has been planted in every spare bit of land.  Other access to the field is much more restricted than in the past.

I suspect they don't like the risk of driving through tall grass.  They prefer to joyride where they can see any obstacles.  Hidden dangers are expensive when they hit them so they avoid the tall grass and corn.

If they started driving through the corn to get to the field, the farmer would take steps to prevent that.  The ATV users know that.  The culprits are opportunistic.  They take the easy way.  Take away the easy way or provide hidden obstacles will be deterrence.

Suggesting that a video of the field was taken from an illegal altitude is neither correct or appropriate.  It does not appear from the video that the person making those invalid comments, was there at the time.