Dgarretson: Making a twisted pair lowered the inductance and nominal impedance of the cable as compared to running the cables spaced further apart. Since impedance typically rises with frequency in most audio circuits, making it harder to pass signal as frequency climbs, and inductance rolls off the treble response, the steps that you took helped to negate those potential problems. That's why you can hear the changes that you made in a clearly audible fashion.
Having said that, unless you can maintain near identical conductor lengths and a VERY consistent weave, i would stick to using the twisted pair configuration. Even going this route with multiple conductors can be tough. That is, it becomes difficult to control the internal geometry of the multiple conductors within each leg of the cable.
If you are trying to optimize a design using the parts that you've already got, you might want to try going the spiral wrapped star quad approach. This will require using two more cotton sleeves per cable, meaning that you would need four more total.
Use two conductors per leg and stagger the polarities of each leg. In other words, use 2 pos, 2 neg, 2 pos, 2 neg in an alternating circle arrangement. Once you've got the four individual bundles somewhat anchored together, apply a slight but consistent spiral twist to the entire length of the bundle.
This approach will lower your nominal impedance, offer improved power transfer, offer increased transient capabilities, broaden the bandwidth of the cable, reduce EM radiation from the cable itself, offer a reduction in potential RFI susceptability, etc...
This approach is about as good as you can get using what you have without getting far more complex and time consuming. Whether or not you like the end result would obviously be a matter of personal preference. Sean
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PS... Your aggregate gauge size is appr 18 gauge for the four 24 gauge wires per polarity.