If you think that it needs to go, get many bids from reputable companies with references, which you check, for a drop and leave.
Explain the parameters. Looking for cheapest option without damage to houses. The lawn can have holes punched into it. I don't care about that bush, that is important to save, I'll transplant that before you come, I'll move whatever is in the yard that needs to be moved.
You can cut it up yourself.
I'm a Stihl guy. I love the 361, but would love a 441, and even more the not yet made 661. The anti-vibe is the key to me. If you have not joint problems, a 036/ 360 would get you through it all with some cutting from both sides of the log.
A 044/440 might be a bit much for a homeowner.
I'd say buy a 361 for about $600, then sell it for about $400 on Ebay when done, keep the smaller saw for your occasional needs.
buy chaps, eye and ear protection. Stihl has a DVD for about $6 that is a decent overview of use and maintenance. Buy bucking wedges and use them. A claw hammer is enough to pound them, but a 3-5# hammer would be a bit better.
Around here anybody can rent a 60' lift at a local rental company, but you need a bond for anything bigger (from Hertz, company policy). I'd say, don't do it.
Hire out the more skilled work, tackle what you can. Feel good about being wise enough to make good choices, and having the initiative to tackle what is reasonable.
A good climber would probably not use a lift, which would save money over such specialty equipment like a 90' bucket truck. I'm guessing to rent a 100' lift so you can drop small pieces without rigging is going to be $600+ per day, and you'll need more than one day, I'll bet.
You neighbor has the gear, but anyone can buy gear. The key is the knowledge and experience to not kill oneself or crush someone's house.
Let us know how it goes.
Would be interesting to see more pics, before, during, and after.