How much water does my tree need during dry conditions?
I would strongly suggest sending your neighbors a certified letter stating that, per your earlier conversation, you consider this tree to be a hazard due to its proximity to the power lines. Then, when and if something bad does happen, you will have a record of having informed them of it and they won't be able to say "we didn't know."
You say the county has told you it is the neighbor's problem. Did you contact the local electric company? They should care very much about the situation.
I would also recommend taking lots of pictures showing the proximity of the tree to the wires and that it is obviously dead.
Dead trees do sometimes stay vertical for a very long time, but it sounds like a tense situation for you. I understand your desire to not inflame the situation, but it doesn't sound like there is anything more you can do that won't have the potential to do so. So it becomes your responsibility to look after your own interests in the most reasonable way possible.