I can't stress this enough - the jrc4556 has a high input offset, so "time, energy, research, and experimentation" is just silly.
The resistor from noninverting input to ground is 100k, a fairly normal value and the same value seen in the CMOY. This is textbook stuff. Doesn't affect the sound.
Since the input offset is so high, the other two feedback loop resistors MUST equal roughly 100k when paralleled.
This wasn't a matter of selection - they decided how much voltage gain they wanted and did the math.
This is textbook stuff, and doesn't affect the sound.
Instead of the voltage divider you see in most cmoys, they just use two 9v batteries with the center tapped as virtual ground. This works, but you get offset if one battery drains before the other, which does happen fairly often.
Where the cmoy has power reserve caps, the RA-1 just has 112nf ceramics. This is interesting because this is the sort of value you'd generally see right up against the power pins on the opamp, merely to stabalize it.
The stabalizing bypass caps are, again, textbook stuff, and doesn't affect the sound.
They probably chose the 4556 because it's New Japan Radio's top of the line for high-current service. It can really sink some juice.
So, the design choices they made were to leave out large power reserve caps - which can make the bass sound a bit thin - and to use absurdly large input coupling caps, which can add a bit of euphony.