I was looking around to see what sort of discrete circuitry would be required to convert from single-ended to differential (balanced), and the simplest representation consists of 3 resistors, and 2 NPN transistors.
Some additional components will be needed, if operating from a single +18VDC supply, rather than a split supply - since if Vee = GND, and you GND the Base input on Q2, the circuit won't work. I guess the additional components would set the bias voltage on the Bases high enough above GND, to flow enough current through the Collector resistors, so that with no Audio input, the voltage at Vout is ~9VDC.
(From:
https://en.wikipedia.org/wiki/Differential_amplifier)
Two of these circuits would take the single-ended (L+ / GND) (R+ / GND) input, and produce a balanced (L+ / L-) (R+ / R-) output - which could feed the input to your XRK Class A amp boards.
Currently, each of your amp circuit boards has a dual 10K potentiometer, to control L / R volume (by attenuating the input to the amp). So, if you're using two boards, in a balanced configuration, you have to adjust two separate knobs (one for L, one for R) to control volume.
It's a bit tricky trying to determine the best place to connect the potentiometer(s), if the amp can be used as -
Single-ended Input to Single-ended Output
Single-ended Input to Balanced Output
Balanced Input to Single-ended Output
Balanced Input to Balanced Output