If you were to stay far enough away from the trees so they couldn't be pulled over on top of you, doubt anything I own would even pull the anchor chain itself, let alone grub any tree's.
The burn thing isn't something that would bother me one bit, pick a nice winter day with some snow cover on most everything, keeping in mind, this isn't near anything else, its a ravine in the middle of a farm, the nearest building would be a 1/2 miles away and it would have to jump two roads to get to those, which I doubt would ever happen, that and it would have scorch several farms in between which have no corn stalks left out on them anyhow, cattlemen own them and everything is either chopped for silage or round baled after harvest. Only this farmers corn stalks would be an issue, and as I told him, chisel the whole farm when he's done combining and it should be a non issue.
The other thing to bear in mind is this, wait them out, stay away and not plant along the boarder or better yet bid those acres into a set aside program and not farm near this at all, eventually they will fall down and nobody would get hurt, post signs stating to keep out private property and keep those signs up and consult with an attorney and have him or her deal with your insurance company and work a deal out till the trees are safe enough to pile up and burn. Like I told him, he has options and right now plenty of them and to keep calm and bide for some more time.
As for burning standing trees, we've done it before many times, when they are that rotten and if you can get the right conditions that will dry them out, like in the dead of winter and still have snow cover, they really do burn good, the key is figuring out how to get close enough to them to light them up and not get hurt with falling debris. We've also done it in the dead of summer when everything is green and growing full tilt, then nothing else burns in my area but the dead stuff. Rotten tree's burn great, take very little to ignite and once lit, keep burning really well till the top heavy weight topples them over or they burn down enough only the trunk is left standing. We've also burned some that overnight they fell and the next day, there was nothing left but ashes, they burned up completely, then all we had to do is grub the stump out.
D6, I'd venture a guess you have insurance, just call the company your insured with and start asking questions, general ones about liability and see what they tell you, you can also post signs to keep out and don't give anyone permission to hunt for the next few years, after all its your land and you don't have to provide permission to enter. Most insurance companies will give you answers of some sort, some better than others, ask them what to do with the dead trees, eventually they'll fall down on their own, gravity always wins in the end and at the rate ash rot, it won't take that many more years anyhow.