I know you've checked and re-checked it, but when I read this:

So far the *only* time I've been able to get the engine going is when the wires have been in the wrong order - usually #2 and #3 reversed, but that has not been consistent enough to help...

It makes me wonder about this so-called "wrong order." If the engine is having this hard of a time starting in the "right" order, but it managed to start at some point with the wires in the "wrong" order...

It's a simple three steps, and you've probably done it over and over, but...

1) make sure your engine is physically at TDC with cylinder-1 firing (both cyl-1 valves closed), and not TDC with cylinder-4 firing. Now back it up 10 degrees (wrench the engine CCW, standing at the front of the car, to the 10 degree mark).

2) set the static timing @ the dizzy. It doesn't matter if the distributor drive gear was put in 180-degrees off, dead on, or 2-teeth off. I use the continuity tester on my multimeter to find the exact moment the points open up as I twist the distributor CLOCKWISE (to mimic the action of the rotor turning counterclockwise).

3) Wherever the rotor is pointing is where your #1 wire goes. Put the cap on, plug that #1 wire into the right spot, and, working your way around the cap counter-clockwise, plug in the rest of the plug wires: 1-3-4-2.

I'm not trying to sound redundant and re-post what others have said, but when you say you've actually been able to start it (if only once) with what appeared to be the wires in the "wrong order," it makes me wonder...