The capacitive loading specifications of the phono inputs of the 160 and 162 are odd, to say the least, while the corresponding figures for the 116 are much more reasonable:
NAD 160 & 162:
Moving magnet: 47K, 470 pf
Moving coil: 100 ohms, 1000 pf
Moving magnet: 47K, 200 pf
Moving coil: 100 ohms, 50 pf
I don't know what kind of cartridge you are using, but given the facts you described it seems likely that the very high input capacitances of the 160 and 162 are major contributors to the problem. Especially if you are using a moving magnet cartridge, but conceivably also if it is a moving coil.
So I second the idea of a separate phono stage, preferably one providing low input capacitance and (if you are using a moving coil cartridge) flexibility of resistive loading.
Good luck. Regards,