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Almost Cap'n Bloggs. If the speed brakes are popped at high levels the Vma bar rapidly shoots up to (and if used too agressively, beyond) your current airspeed, without a corresponding reduction in speed. Thus they do little to reduce an overspeed but rapidly give you another one. It's not until you get down to 360 or so you can use them with relative impunity. Therefore, short of a climb (above the certified ceiling) there is little you can do apart other than closing the thrust levers to reduce your airspeed."
Pitdown, I agree with you in relation to SB use. At very high levels it absolutely does not make any sense to use them
But in relation to the thrust levers, why closing them considering the ATHR is engaged?! Why not just monitor the ATHR and see if it is simply doing is job?
What I teach to my students when flying at very high levels is:
1. Don't touch anything (which means, sidestick, thrust levers and SB)
2. Monitor the ATHR (and corresponding thrust reduction)