The Niles needs at least 30 Watts of power draw to switch reliably so I guess that means the 976 doesn't draw 30 Watts.

How are you turning on your amp? I'm guessing that if you use the trigger out of the 976 to your amp and have the Niles current sense the amp it should work. Though you will have to be careful not to exceed the max current draw for the Niles.
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975/7075/SMS-1
Aperion Verus Grand Towers & Bookshelves, Verus Forte Center, Infinity Surrounds, Ultra-X12
Oppo BDP-203, XBOX360, Xbox One
LG 65" OLED
RR2150 w/Klipsch SCR-2