>Is it possible to modify this unit so that it has true balanced inputs, and without degrading the signal?
Sure. Use a Jensen input transformer or build an active circuit around an INA134.
If I had an active balanced output I'd just wire + to the RCA center pin and ground to ground - just 25' of interconnect is not enough to raise the noise floor of a decent solid state amplifier (I used to run 25' of interconnect between my preamp and active cross-over, because that was a lot less mess than 25' x 8 speaker cables)