The Pioneer doesn't have balanced outputs. Using RCA to TRS connectors instead of RCA to TS shouldn't make any difference. You could try it, but don't expect to the hum to go away.
What you're probably hearing is a ground-loop where your amplifier is seeing ground at a slightly different potential from your receiver or source device. There are lots of things that could be causing it, but the most common source seems to be the cable TV (or satellite) coax running into the system. Try disconnecting that and see if the hum stops. If that's it, you'll need to have the coax shield properly grounded.
If that's not it, you'll probably want to do some reading on the subject before digging any deeper into your system.