"... top management may very well throw lower management (or worker bees) under the bus, for making trouble."
...
They may throw the bully under the bus, or they may throw YOU under the bus, for complaining! I would trust HPE management to make good judgment calls here, just about as far as I could throw them! Which is to say, not at all! Unless you can make a bullet-proof case, that can be taken to court if need be.
You can always tape-record secretly (stick a recorded in your pocket), and seal your lips forever, about that, if you live in a state with silly laws surrounding this issue. Then afterwards, transcribe word-for-word, to paper copy, sign and date it. Now you can state, straight-faced and honest, with paper copy, that you transcribed ("nearly" 100% accurate, ahem) it word for word, after your conversations. If the bullying is bad enough, those PAPER copies of your conversations will be worth their weight in gold!
If you're a member of any kind of "protected class", you may prevail, in court or out of court. If you're not protected-class... Good luck!