Coils overheat with merely turning key on

What wiring did you fix? The only reason why the coils would get hot as soon as the key was turned on would be if they are being triggered on all the time. Below is the schematic. Each coil should have battery power to pin 3, Ground to pin 2 and the trigger wire goes to the ECM and only gets a signal when told to fire,

The most likely suspect that would trigger them on all the time would be a failed cam sensor, or bad ECM. If it was a shorted trigger wire it would have to be all of them which means a bad ECM.
You should be able to see the ignition pulses to each coil with a test light on the trigger pin. If they each glow as soon as you turn the key on you have a problem.
Unplug the cam sensor, do they stop and cool down? If yes the sensor is faulty.

If it is the ECM there is not any repair, just replace. Mainly because there are no schematics available to "the public" and the parts can be hard to source.

I have been watching Irma, stay safe and return when you can. We will be here.

Have you unplugged the cam sensor to make sure it isn't shorted?
With a drop in ECM at around 200 bucks I would simply swap it for a reman or a used unit for testing. But for either of those you still need to be able to program the unit when you install it, unless you can get one that is a drop in.

ASCD is Nissan speak for cruise control. Automatic Speed Control Device. It's a box hidden behind the dash.

What happens if you swap the coil to a different cylinder? Does it still get hot or does the problem stay at cylinder 1?