Hmmm....so if you don't have the knowledge and gear to do it safely.....hmmmm.....well then screw safety, get the ladder. Or maybe find someone who has the knowledge and gear to ground it safely.
Naw....I was trying to insult you for advising a guy to put himself in a dangerous spot. If that makes you not like this place....well, I'll get over it.
I don't think you're getting what I'm saying here.
"Safety" is a relative term. You're never "safe". Everything has varying degrees of risk. Each person must evaluate the level of risk that they're assuming when doing things like this.
In this person's case they've evaluated that there is a certain risk that the tree could fall on them while riding underneath it (remember, the tree crosses a trail). They've decided that the risk to themselves for cutting this tree down is worth mitigating the repetitive exposure to the risk of riding under the tree.
In this person's case, they may not be able to afford to hire a climber to take the tree down properly. People do things like this everyday and rarely do you hear of injuries. As a matter of fact, I'll bet that you think ladders are so dangerous because you only hear of the bad happenings. Whereas, you think climbing is so much safer because you're exposed to a lot of successful climbing stories if you're in the tree industry. That is what the professionals use.
Now I know what you're thinking, "The professionals climb because it's the only safe way to do it". You're wrong, the professionals climb because there is "less" risk by climbing, but it's not completely safe. The professionals can afford to outfit themselves with climbing gear and do the training because they will use it every day and it will easily pay for itself, especially because there are some jobs that ladders really are dangerous on. For somebody that doesn't cut trees for a living the climbing isn't economical. So when possibly, using a ladder with some common sense is a slightly more risky alternative. Is it completely safe? No. Is it extremely dangerous? Not if you use some common sense. In the event that your common sense tells you that using a ladder IS dangerous then hire a climber or leave it alone.
The reason ladders have a bad name while cutting is because people don't use common sense all the time. Cutting a branch off 20' up a tree certainly has a LOT more risk than 6' up a tree. The size of the branch also plays into the risk; as well as the shape of the branch, horizontal/vertical etc. In this case, if the tree-branch were 6-7' off the ground as I thought the picture looked, it isn't "loaded" in any weird way, and it's a good straight branch it should be a straight drop to the ground after cutting. It's not going to spring back past the tree. Now, being as it's 10-12' above the ground it very likely could drop in a way as to do that. There is more assumed risk cutting from a ladder at that height. (hence why I said I wouldn't recommend it at that height).
So going back to the risk thing (still assuming the branch was low); the cutter, in this case has to evaluate the level of risk that the butt will kick back as he has no other option to remove the other risk of riding under the tree. It's all a balancing act.
Is the repetitive risk of riding under the tree > the expense of hiring a climber to remove it? If so, hire a climber. If not proceed to the next.
Is the repetitive risk of riding under the tree > the risk of cutting it down by himself? If so, then cut it down.
Wasn't that simple?
BTW, if he really thought the risk was great enough that he needed to hire a climber then he wouldn't be here asking about it.
So we go back to cutting it down himself. How would you do it without heavy equipment (dozer) and without climbing gear (we'll assuming that he doesn't have any).
BTW, on pulling tops out like that, yeah, they take a lot more force than expected to pull them out but if it's really only hanging by a little bark like he said it should come down pretty easy. I've I doubt a 4 wheeler would do it just because it's not heavy enough to stay on the ground with a cable pulling up on it at an angle like that, but the op's tractor he mentioned should do quite well at it.
My uncle cuts wood for a 2nd job (has his own sawmill) and I've cut plenty of wood in my day as well. I can tell you that a top like that will come out easy as pie if he has the right equipment and knows how to pull it. I've seen it done in person hundreds of times and a lot of people no here could say the same thing.