Now, I haven't been an arborist as long as some others on this site, but I am a tree fanatic and am constantly observing trees in both their natural setting and urban settings. One thing I do pay close attention to is dead trees and how long they stand on there own in both situations... I realize that different species have different levels of decay resistance, and of course every situation is different so this is always taken into consideration.
When I look at a dead urban tree such as this it immediately gets a slightly higher price tag due to the hazard level. First choice should always be to flop it if there is room. When deciding to climb a tree or not I figure, "are the Lilacs underneath worth the price of my life if this tree fails with me in it?" NO! Rigging and shock loading a dead tree are beyond mindless if you are tied into that same tree. If the landscaping is that important, or if the tree is over a house then the customer must agree to the price of a crane. The tree in question can easily be removed in sections with no shock loading at all using a crane (providing there is room, and all other obvious variables involved). If worried about the baserot... toss a throwball in it, pull up a rope and give it some gentle to strong tuggs... observe how the tree responds, i.e. swaying movement... this will give you at least some idea of the soundness of its roots. Also, when deciding whether or not to climb, consider this: determine the actual weight of the entire tree, (wood mass) compared to how sheltered it is (wind resistance) compared to how long the tree has been standing dead/rotting, compared to the species (wood strength). Now fugure how much you weigh... you won't be shock loading it, so your climbing wieght will be "COMPRESSION" stress (very important). Do you think that your compression/climbing stress will outwiegh the standing mass and wood strength of this tree? If so... don't climb it: rent a small skylift, or bucket truck. One other note to remember when flopping a dead tree... dead wood doesn't hing the same as green wood. I've seen dead trees break under their weight in the wrong direction once the back cut was deep enough.
Climb safe.