A boom pole and a length of 1/4" chain has turned into one of my most useful attachments for my tractor.
After I drop a tree, I hook the chain about 6' up from the base of the trunk, lift it off the ground with the boom, then slice pieces off of it like it's a roll of Bologna. When I cut up to the chain, I set it down, move the chain up and continue cutting,...limbing as I go.
You can dissect a tree pretty quick like that without having to worry about the saw getting in a pinch.
I drag the tree back to the burn pit before I start cutting it up, get the fire going, and just pitch chunks of the tree into the fire as I cut them off.
A good "no drama" way to start a brush pile fire is with those Duraflame logs that people burn in the fireplace. They burn for about 2 hours, or so. Put one of the bottom, light it up, then start stacking limbs on top of it. They'll even get green wood burning and you don't need to keep dousing the fire with diesel fuel.
I used the above method to burn a 25' Spruce tree that had died in the front yard.
I had it cut, dissected, and on fire in about an hour and a half.