Obviously tree work is a dangerous kind of work, and it should be said, its best left to experienced hands for valid reasons. However if you are comfortable working off a boom lift, basket or from a bucket truck, and have a plan to safely dismantle the tree, confident in your ability, I would not hesitate if tasked with doing the work, that is if you like you say, if insurance won't pay for a claim on that, either way, sounds like it has to come down.
Given the certification, you must be experienced with these, so that helps quite a bit.
Personally, I've been on most late model JLG articulated boom lifts, scissor lifts, non articulated, many Snorkel lifts as well, my only concern with this situation is the footing, how level the ground is, and the plan to dismantle the tree in safe increments. Those darned limbs will be unpredictable, make a wrong move, good idea to really look it over first, I try to do that with problem trees, if its out of my league or the equipment I have, I simply walk away from it.
There was a fellow on live leak who was up into the lower canopy of a tree, he cut a limb off and the butt of it came down into where his leg was in the crotch and busted it but good, it was a flapper with a compound fracture through the skin, something everyone should see if contemplating this work, he was not even tied off, dropped the saw to the ground and then had to be rescued, and his leg when set, looked like a shark bit the darned thing with the football shaped incision. Seems he did not think that one through.
Those JLG 80' articulated units are really nice units, I had 3 out on rental for almost a year on a new courthouse job in Queens NY and compared to scaffold or anything else, they cost a lot per month, but the productivity made up for it. Just a great piece of equipment for working at heights, this reached up 5 floors, and I put 2 ironworkers in each basket. Make sure to size it accordingly, over is better than under.
I would hope the insurance company would pay on this, and you have a tree service do it so as not to worry about being in harms way, these can be intimidating at first glance.