How are you going to connect the amp to the HK? The input to the amp has to come from the HK from the pre-amp. The HK does have analog output to allow feeding an outboard amp. You have to remove the jumper pins and connect the preamp outputs to the amplifier input and then connect the preamp output to the input of the new amp. You can't use balanced cables as there are no XLR connectors on the AVR 7000. Get a set of 5 interconnects from BlueJeans Cable long enough to connect the AVR to the amp. You can use the same speakers cable you have now but each speaker has a Positive and Negative side and has to be connected to the correct terminal. The red terminal should be connected to the positive side of the speaker and the black to the negative side. Do this for all 5 speakers L,R,C,SL and SR. Copper Monster cable is fine just make sure the polarity is connected correctly and that no stray wires are touching anything except the terminal.
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Music system
Model 990/7500/Magnepan 1.6 QRs/Technics SL1200 MK2/Aperion S-12 Subwoofer/OWA3/Sony NS75H DVD
APC H15 Power Conditioner

TV System
Large Advent Loudspeakers/ Polk center/Monoprice surrounds/Panasonic Viera 42 inch/Onkyo HT-RC260/Sony BDP S590/Directv


Home Theater System
Onkyo PR-SC886/Outlaw 7125 Klipsch RF-82 L/R,RC-62 center, RB-35 SR/SL, BENQ HT1075, Outlaw LFM1-EX/OPPO BDP-83/Directv
Harmony ONE
Blue Jeans and Monoprice interconnects
APC H15 Power Conditioner