I have the same combo, and I think the KGSS is Class A, which means turn it off. I leave the 007's plugged in always to save wear-and-tear on the connectors.
When I come home at night, I turn the KGSS on, and give in 20 minutes to warm up. I have tried longer warm-up periods but detect no difference in SQ. When I am finished listening, I turn the vol to zero, and shut the unit off.
My wife listens to the same CDs via balanced pass-thru on our Beta 22 (we come balanced out of our CDP, into the Beta 22, and pass-thru to the KGSS). I treat the Beta 22 the same way, knowing for sure it is Class A and this is the right thing to do since Ying, the bulder/owner at YBM Audio, told me so! We keep the balanced /markl/Lawton modded D2000 plugged in to the Beta 22 for the same reason -- protect the XLRs. The Beta 22 goes on and off right along with the KGSS.