After-hours conversations among staff members now frequently center on how unpleasant NM is and how the dynamics of a previously pleasant workplace have shifted since the arrival of NM,
Avoid this! Nix it wherever you can.
And focus on the info you're not getting.
And since she's unpleasant, feel free to be as pushy as you need to be. Feel free to stand by her desk and watch her do whatever it is you are urgently waiting on. Feel free to cc: the boss about whatever it is.
Is the best approach to document (or comment when I am sure to be overheard) and send things up the ladder, even though they're not inclined to do anything about it, or to say something to NM directly?
Don't do this obliquely.
First go straight to NM the normal way. Tell her what you need and what your own timeframe requires. Stress that this is so you can meet boss's]
Then give her time to actually do it. When she misses that deadline, go back to her and say, "I need this now. Please give it to me." And then stand there until she does.
If she balks and insists that she won't, then go back to your desk and write an email that says, "Boss, I need this from NM or I won't be able to make the deadline you've given me. I've requested that she expedite it, but she says she's too busy because of Reason. What should I do next? Should I do it incompletely without the info from her, should I wait until she's able to do this?"
And if nothing happens in a short time, you go directly to your boss and say, "Did you see that email? What do I do?" And if he says, "get that from NM," then say, "I'm going to ask that you speak with her directly so that she knows this is important enough to stop her other tasks."
also, re: this:
I object because A. It's dumb (although I haven't shared that with the office)
Nothing is inherently dumb.
"Dumb" always has other reasons. It's costly, it's wasteful, it's fixing a problem that doesn't exist, it's complicated, etc.
Just as with her unpleasant personality, erase this. Try to get it out of your own mind, even, but never ever let it seep out, even in tone of voice.
People are allowed to be annoying; they're not entitled to refuse to give you the info you need to do your job.
Ideas are allowed to exist; if you're going to label them "dumb," you ought to be able to delineate exactly *why* they are dumb.