First, power loss (resistance) is a function of voltage and current. V = I.R. (No, not the one on Cartoon Channel. :) If you increase the current, but keep the voltage the same, you must decrease the resistance.
In practice, what you usually end up doing is increasing both the voltage -and- the current, allowing you to deliver much more power at (proportionately) less cost.
This is one reason some European countries opted for a 13 amp, 250-volt system. The loss is much less, per unit of energy delivered.
The problem of California (and the US as a whole - don't imagine that this won't affect other States, over time) can therefore be easily resolved. Simply ramp up the power grid, thus delivering much more of the power that's actually generated.
The second part of the problem is how to reduce the resistance -in- the cables. Copper is being replaced with aluminium, which is a good place to start. Chip manufactuerers are going the other direction, to improve performance. The only benefit aluminium has is that it improves the quarterly figures, increasing the value of the shareholders' stocks.
Actually, the best metals to use would be silver and gold. Their conductivity is vastly superior to copper. Yes, silver is also very reactive and isn't exactly strong. That's why you'd probably want something like a silver glaze, with some sort of polish to prevent it oxidizing. (You don't need a lot of silver, as the current is carried on the surface, not in the core.)
If you wanted to switch to something a bit more exotic, there's no actual reason to deliver current that way at all. Make a -hollow- cable, and use it as a wave-guide. Blast electrons down it. This "simulates" the likely behaviour of super-conductors, without needing to produce ultra-cold temperatures.
The main problem with this solution is that it would require replacing a lot of cable, as it's not a trivial upgrade, in the same way the others are.
The bottom line, though, is that de-regulation, combined with inane, archaic and obsessive cheapness has created this crisis. Only when the energy companies and politicians are dragged, kicking and screaming, into the present day, EVEN IF THAT MEANS RAISING TAXES!, will any solution be even remotely considered. A medieval mind CANNOT fix problems that don't exist in a medieval world.