The current strategy can only bring resistivity down to about 400 Ω. Which it does in a matter of seconds, by the way, but 400 Ω is not a wire; 400 Ω is a resistor. The reason it can't go any lower is simple: as resistance decreases, heating and electrolysis increase, and the gases created within the channel are forced out, preventing the copper from forming a continuous wire.

Of course, I could work around this in a later version of the process, but I have a better idea. High voltages can easily fry sensitive components, but there's something that can't: solder! Not your regular solder, of course, but Rose's metal, which melts just below the boiling point of water, that also just happens to be the usual bed temperature for printing ABS...

Picture this. You start printing the PCB in ABS; the printer creates a small funnel within the piece, then pauses. You put a small bit of the alloy in there, which immediately melts, filling the funnel. The printer then goes on, covering the cavity with more layers of plastic. Without cooling the bed, you put the components in place, and you inject air through a small hole in the print, while removing the same volume through a second hole. The molten metal is forced through tiny channels and wets the components, soldering their pins, possibly to actual wires you have also placed.