If you are going to go into a questionable area, the least I can say is to leave the place better than you found it. Pack it in, pack it out... and pack out any obvious garbage and trash that others have left behind.
There is a local road here in my town that is a well known illegal wheeling location. The land off one side is completely illegal, being a wildlife management area, yet local troublemakers constantly rip it up. The land off the other side, my club has written permission for as long as we pay the daily use fee (which is reasonable.) Troublemakers still rip it up. I've found unattended bonfires surrounded by dozens of scattered beer bottles and cans a few times. The road down the middle is legally a public town road and is even on the map, it is a common area where many shady locals do their illegal dumping. I often run up and down that road for fun (we don't have any wide open desert type areas to do go-fast in...) and I used to get the evil eye from residents a LOT. Then they started noticing that I always went in with an empty bed and came out with a few junk tires, or a couch, or a bed heaped with trash, and I haven't been glared at since then. A few even wave now.
I would still recommend either getting written permission or staying on any public rights of way within the property, really. But being viewed as part of the solution instead of part of the problem (visibly carrying more debris out than was brought in) can go a long way toward a positive public opinion and IMO that can lead to more access as opposed to less.
Hell, maybe you guys could get a deal with the owners, they put dumpsters in some secured nearby location and you're allowed to run the trails as long as you hold a monthly cleanup day or something.
