This is why I dislike electronic ignition. Even when it's not the problem, it always lurks in the back of your mind making you second guess what you are doing. I got a 123 distributor on the shelf for my car so I hope your problem does not end up being the distributor.
It's hard to diagnose running problems when you're not with the car. I don't know much about those Webbers but I think they have 2 idle jets and 2 mixture screws. You said you covered the top of the carb with your hand and it died. Did you cover both sides or one at a time and did you cover them all the way or partially?. This is the way I do it on Weber IDF carbs. I partially cover one throat at a time. The slight restriction over the throat will create vacuum below your hand and pull fuel through main jets (this is how the choke on a carburetor works). Under normal idle conditions, the vacuum is under the throttle butterfly and drawing fuel through the mixture screw. So if you cover one throat partially and the idle gets worse that throat is probably functioning properly. If the idle smooths out then the idle circuit on that throat is probably not functioning properly or set too lean. You can also use this to diagnose a clogged main jet. If you partially cover the throat and look down it at the same time you can normally see the fuel dribble out of the auxiliary venturi. If nothing comes out then you know you have a problem. This won't work the same on your car because if I'm not mistaken both throats of the 38dgxx feed all 4 cylinders. If you partially cover either throat and either idle jet is clogged the idle should pick up regardless because it will be drawing more fuel through the main circuit compensating for the dead idle circuit. To pinpoint which throat has the problem you can try and slowly turn one mixture screw in until the idle starts to drop. If you can turn the screw all the way in with no effect then you could have a clogged jet on that throat or a very poorly adjusted carb. If you cover the throats completely it will just apply the full engine vacuum the float bowl and blast fuel into the engine with no air and instantly flood it.