Thanks for all the input! To clear a few things up: the branch is nearly the height of a 2 story home, and outstretches about 20 feet. Consequently, a few ladders --- even duct taped together, wouldn't cut it (no pun intended). We'd send up the grandkids, and or do it ourselves but fear the cost of multiple funerals would also be outside our budget as it's clearly too dangerous.
We took to getting estimates from insured places and the median average was over $700 - a few tree services came, took one look at it and declined to bid as they thought it was too dangerous too.
The crazy neighbor took to calling the police each time she saw a tree service provider coming to give estimates.
The police, equally impressed by the 'widow-maker' branches advised us to call the City inspector, who may order the branch cut down and or order the foresty division to cut it down and assess the responsible home owner's taxes.
This of course, is the least appealing option, but may end up where this goes.
Thanks for the certified letter with estimates idea. Since reading that here, we've done that too.
We're sad really. No one wants to be at odds with the neighbors over a tree but the issue here is personal responsibility and in this case, that personal responsibility is not ours to bear.