How to get ATVs off fragile trails?

We have NH property where ATV tracks have caused major soil erosion, root damage, washouts, mud-holes, and made trails 30 feet wide in some places (to avoid the ever-widening puddles). What can we do to persuade ATV riders to stay on trails, avoid poorly drained areas, and register with the land-owners (as required by law)? We put up signs about "private property", as a reminder to be courteous, and they were all stolen. We blocked some hillside trails with logs and flagging and they were all pulled apart and driven over. We don't want to put up fences or have people arrested (yet), but we're looking at over $50,000 to repair damage to our roads and trails.