This is gonna sound stupid I know, but here is what I would do :
To be certain that 12v is still being supplied to the 3 coil packs for the failing cylinders, I would wire up a small 12v light bulb to the black/dark green wire on coil pack #3 ( and ground ) with wires long enough to route out the rear of the hood and tape the bulb to the top of the hood where you can see it. ( reference the schematic in post #4 )
Make certain that the bulb lights as soon as you turn on the ignition.
Then drive the 5 miles and see if the bulb remains lit when the malfunction begins.

1. If the bulb is out at that point, then you are going to have to tear into the wiring and find where the intermittent open in the supply wire is.
2. If the bulb remains lit, then you will have to determine why the PCM is not supplying a ground to those coils when it should. Maybe some other member can help with this, as I haven't a clue how to determine that.