[T3] Mysterious squareback condition.... need suggestions.

[James Lingenfelter]

   I have a '68 squareback, with dual Weber 34ICT carbs. My wife  
drives it much more than I do. About 6 weeks ago she called me saying  
it had started running poorly on her way home from the store, felt  
like it was missing, started backfiring, etc. She got a block from  
home and it died and would not restart. When I got home I looked at  
it and saw nothing other than the coil wire being slightly loose.  
After pushing that back on, it started immediately, idled perfectly,  
I took it for about a 45 minute test run and it ran absolutely  
perfectly. I determined either the coil wire had been coming off, or  
either my wife was going nuts.
   We continued driving it over the last month with no problems  
whatsoever. Then yesterday, my wife was taking it to the grocery  
store..... she said it was hard to start, then ran horrible leaving  
home, so she immediately came back and parked it. She tried later in  
the day to start it and couldn't. When I got home from work, I got it  
started after much cranking and pumping on the gas, but then it idled  
horribly and would die within 30 seconds if you let off the throttle.  
And I witnessed it backfire once through the passenger side carb when  
I opened the throttle from the engine compartment. From randomly  
inspecting things in the engine compartment I discovered massive  
corrosion at the plug wire connections to the distributor cap..... I  
was already planning to replace them since one plug wire had shocked  
me through the shielding recently. I consulted with my brother, who's  
an auto mechanic, and determined that, considering the all-day rain  
we had yesterday, that I indeed had an ignition problem probably  
resulting from poor connections or arcing somewhere.
   So, today I replaced the distributor cap, rotor, and plug  
wires.... It started immediately, idled OK; I let it idle in the  
driveway about 15 minutes, then took it for a shakedown run. I drove  
about 5 minutes, and suddenly without warning, it felt like it was  
running on two cylinders..... not even three, but TWO. Barely enough  
torque to let in the clutch in any gear without killing the engine. I  
let off the gas and it idled very slowly and lopsided, and was  
destined to die.... I revved it, it sounded ok again, and I pulled  
over the first decent place I came to. I shut it off for a few  
minutes. It restarted easily, and ran fine coming back home.
   So this is where I'm at now. I've now witnessed what my wife has  
been trying to describe, and I have no idea what it is. Fuel pump is  
good, recently replaced fuel filters; intake leaks that plagued me  
forever are permanently fixed.... I maintain this car pretty  
obsessively since it's a daily driver. Could it be a carb issue?  
Sorry this message is so long, but I thought I'd relay every detail  
in case any of it helps. Any clues or suggestions will be greatly  
appreciated!
   Thanks,
    Jimmy