Yo, Peter. As frustrating as things may seem, you are in fact doing everything right in what is a more involved fault-finding process than, perhaps, you expected. Been there and done that. These are, after all, old cars. In searching for a solution to your running problem you discovered that the carbs really needed seeing to so rebuilding them solved once source of problems in old Alfas. Webers are great . . . until they're not. Likewise replacing plug wires set aside another problem with old cars. I think you've also ascertained that fuel delivery is adequate so you don't need to worry about that. Check, check, and check.
Before you do anything else, however, you need to check the distributor itself. Is the advance mechanism working smoothly? If not that can be fixed. If you can feel slop when you move the shaft side to side, this means the distributor itself is worn out. If the advance mechanism moves smoothly and the distributor shaft feels solid, distributor mechanicals are good and we can move on.
That leaves us with ignition components. Here's what I recommend:
1. Before you proceed to anything else, you need to check and see if the distributor is in good
If your engine is running as bad as you describe and the problem appeared "overnight" . . . I presume after you installed the new plug wires . . . then you may have inadvertently installed the wires 180 degrees out (as me how I know this). The proper solution is to remove the cam cover, rotate the engine to top dead center---cam lobes point out---and then check to see if the distributor rotor point to #1 spark plug position. If it doesn't someone has installed the distributor the wrong way and the firing order is reversed. The fast and dirty "solution" to this is to re-install the plug wire make the #4 position #1 and so on.
If you don't want to pull the cam cover, you can go directly to the plug-wire swap. It's entirely possible that someone has installed the distributor the wrong way and compensated by just changing wires. Happens all the time. As I say these are old cars.
2. If the plug-wire swap doesn't work, then you can move on the 'Plex components. Replacing the coil is a good idea. (Robert Rogers, a noted Alfa race-mechanic in Dallas recommends using an MSD Blaster non-ballasted coil---'Plex ignitiions will run just fine without ballast resistors, btw).
You can also take it to an AutoZone and have them test it for you. If the coil is good, you can move on to the GM trigger which is mounted on the 'Plex heat-sink. A few years ago I had AutoZone test several of these that I had collected in my tool box: fully half were bad. Fortunately, there are excellent aftermarket triggers widely available.
I installed an Accell trigger (thanks RJ) which only costs a little more than the generic triggers of indifferent quality. If the plug wires are installed in the right firing order, the coil is good, and you've installed a new GM trigger, everything is in order and you car will start and run properly. (Please note that I haven't mentioined the 'Plex sensor installed in the distributor. These seldom fail, even after decades of use. However, if everythng check out and you still have rough running these sensors are not expensive and can be obtained from most Alfa parts vendors.)
3. Bob now has his cell-phone back (long story) so you might want to give him a call and ask him to check your distributor. Last that I checked he had a box of 'Plex parts in his shop.
Here's a link to a thread I posted several years ago that shows how the 'Plex distributor is put together.