Have you tried different plug wires or tested the ones you're using? Are you sure the contact inside the boots is actually connecting to the cap's contacts and spark plug contacts?
Not dumbing it up... sometimes it's easy to get carried away and forget the little things.
Okay, what are all the possibilities? These: Coil, Igniter, IGt wire from the ECU to the igniter, CPS (cam position sensor in the distributor providing inaccurate info), bad wires, bad dist. cap, bad rotor, poor connections in the spark plug wires.
A bad ECU, or CPS should give error codes pretty much every time. A bad igniter may not, but it shouldn't be so perfectly off.... but I could be wrong. A bad rotor usually causes weak spark and intermittent misfires on ALL cylinders. A bad cap CAN cause what you're seeing depending on what's wrong with it. Bad wires or poor connections can definitely cause what you're seeing. Spark plugs not properly grounded (not terribly common) can cause similar problems too.
I would start with this: unplug the wires and on both sides push the wire into the boot so the contacts are much further forward and are sure to make good contact. When you reinstall them push the boot hard enough that once the clip connects the boot will slide forward over the spark plug and over the cap's outlet. NEVER remove spark plug wires by pulling on the wire!
Then, failing that, pull the cap and rotor. Clean all contact surfaces thoroughly with a brass wire brush.
If still no good, try installing a better ground in the igniter:
IGNITER GROUND... crispics - SupraMania (That's for the GTE igniter, but I've been told the GE igniter is similar and just as poorly grounded.)