Average quality 12vhpwr cable uses 16 AWG wires, and I think they are quite flexible, the bulkiness comes from the fact that it is 12 wires clamped together.
I think a simple scale up of a 6-pin with 10 AWG wires, or 8-pin with 12AWG wires should be Okay.
They have 80-90 total amps capacity in terms of safety, and okay flexibility.
And one wire could at least withstand 20+Amps...
A simple amazon search gives me roughly the same price for 12 AWG and 16 AWG wires, hence cost isn't the problem.
10 AWG costs twice than 16 AWG but is also uses 1/2 number of wires so they costs roughly the same.
One more observation.
Noticed that both the burn and der8auser's hottest wire all come from the nearest pin from PCB
That pin has the shortest 90 degree bridge behind the connector, hence least amount of resistance.
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