Up side: no offsets, no mortar ooze that I can see; to be honest, looking up from the thimble I almost wonder if the joints are mortared at all. As far as attaching the liner to the bucket, remember, I'm a biker from way back too- I have a closet full of 2-ton ratcheting tie-downs. If it can hold a 'Glide behind my truck at 90, it should be able to get a liner up 30'.
Plan for pulling the liner down consisted of tying a rope to the attached tee, reaching through the thimble, and, well, pulling. This also eliminates the 'guillotine' risk since the tee has a rounded edge like a coffee can.
You can toss the liner on the roof if you like, but remember the stack is 10' above the roof, so that might not be helpful.
Angle grinder with all kinds of blades- yup. I can cut a brick or a Buick in half if necessary. Sawzall too if you wanna get medieval on it.
I am most concerned about the clay thimble... tempted to just chisel the opening bigger, but that takes me deep into uncharted waters. BBart pulled up the best photo I've got in his post above; up to now, the crimped end of the stack was just jammed into that hole and held in by tension.
I think the walkies will either be two cellphones, or Mrs. Blue standing in the doorway yelling in relay.
And have a pocket knife and tin snips up there with ya.
I have a tool bucket laid out that will ride up the first trip. Big orange Homer bucket with lots of little pockets attached. Also have a belt with pouches if you prefer.
Edit: Oh yeah- the bucket will reach above the chimney just as well as next to it, so why not just position yourself above the flue and drop the liner in an arms-length at a time? Take a look at the specs for the lift- that thing will get all Kama Sutra anywhere around the chimney you want it to.