Unfortunately you wasting your time talking with NHSA. They are not concerned at all with any trail issues. Their action this year in taking $12 of each club membership fee as a "transaction fee" is nothing less than extortion and only helping to sink clubs financially.
You need to start with the NH BOT and the clubs themselves. The NHBOT staff are the ones that negotiate the land use contracts with the large landowners and the clubs have the trail agreements with the smaller landowners.
Having been a snowmobile trail master for 7 years and now an ATV trail master for 5 years, I can tell you that one of the major concerns of ALL landowners (large and small) is off trail riding.
On all of the new trails that I have built or rebuilt since 2007, I have included physical barriers on all side trails to make sure people stay on the main trail. When these barriers are removed or breached, we will go in and fix them on a priority basis. If someone cuts a new side trail to get around a barrier, we will block that. If problems continue, we get Fish and Game involved or use game cameras to find out who is causing the damage.
This is part of the commitment that must be made to get new trails opened. I don't know any landowner that says "go ahead and put the trail in anywhere that you want". Some landowners will specify exactly where they want the trail. Others will ask for our recommended route. But in the end, we agree on the trail location and provide the landowner with a detailed map that shows exactly where the trail is going along with the location of all bridges, culverts, gates and rock barriers. In addition to our club, the landowner gets keys to all gates.
I do not forsee any easy way to open up off trail riding. In addition to the sensitive environmental areas that need to be protected, lets talk about the practical aspects.
Just look at the tree damage from the wet snows that occurred this year. Even if you were able to get landowner permission to run on an ungroomed trail through their land, who is going to maintain it? I can tell you that cutting trees that bent over and frozen to the ground is not only dangerous but extremely hard work.
On a groomed trail, the club normally uses the club groomer to help push these trees aside once they have been cut up, but that won't be allowed on ungroomed trails. Having begged for help in clearing our groomed trails over the past 12 years, I doubt very much you will get any of these riders to show up and spend a day hauling a chain saw through 2' deep snow to clear downed trees so they can ride a few miles of fresh powder. Its not much fun doing this work even when I have the groomer. At the end of the day, you are totally wet and exhausted.
How about washouts? On our main trails we spent thousands of dollars putting in bridges, culverts and ditches to control water. What do you think those unmaintained trails look like right now after the deluge of rain that we just got? I am sure there are dozens of 2' deep washouts all over the place.
Right now the only legal off-trail riding that I know of is in Jericho Mt. State Park. All of the ungroomed ATV trails make great places to hone your off-trail skills. But even there, you may find downed trees or washouts blocking your way so be prepared to cut your way through or turn around.