As I said *way* earlier, the poor man's alternative is to let the wires individually rotate at the far attachment point. If periodically, yo relax the tension and give the wires a shake, most of the unwanted twist will come out by spinning the bearings.
You cant really use the hand-ropemaking trick of putting all the twist you want into a single strand of about four times the desired length, then while maintaining tension and twist, doubling it back round a bar to its attachment point, hooking it on there and pulling it through till the three parts are equalised. seizing the strands tightly together at each end, making sure they are lying straight, then twisting it in the direction it wants to go to lay up the strands evenly while relaxing the twist in the individual strands.
If you tried that with wire, the initial harsh twisting would fatigue the strands and probably damage the insulation, then there'd be too much friction between the insulation of the different wires for them to take up the lay nicely.
For a wire laying machine 'lite' that can only do fixed lengths you need a number of equal sized gears running in bearings in a ring that can rotate. Each gear has a hook attached to its shaft to secure a wire to. A center gear of the same size can be driven while the ring is fixed to pre-twist the wires, then a brake applied to the center gear, and removed from the ring so it can be driven by a pinion to lay up the strands. This arrangement removes the need to twist the far end while forming the lay, however it makes it difficult to use a Top to get a consistant layup. Pure unperfumed Talc is your friend - it will lubricate the insulation and make layup far easier. IIRC It can be built with off-the-shelf parts using Meccano,, though the base plate should be bolted to a sheet of 1/2" ply to get enough rigidity, and the hooks will have to be bought at a hardware store, unless you can bend hooks in the ends of 4mm tempered steel rod without the length of it getting bowed.
Edit: I got the gearing wrong. During the layup phase, the center gear would need to be driven in the same direction as the ring at twice the speed since the purpose is to keep all the hooks in the same orientation while rotating the ring.