What does this power designation/rating mean, and do I need to custom-build a power supply to provide it?
There are two solutions for this problem - 

1)Use two transformers - one for 60VAC and other for 9VAC

2)Make a custom transformer having two secondary coils - one for 60VAC and other for 9VAC. This is a single transformer with 2 wires on primary side and 4 wires on secondary side(two for 60VAC and two for 9VAC)

There are solutions for splitting AC. But are costly. Best solution is to use transformers.

I have also faced a similar situation in building audio amplifiers where the power amplifier needs 22V and the filter circuit needs 12 volts and the solution was to build a custom transformer (since 22V was not a standard transformer rating).