A few thoughts for what they're not worth, if it's indeed a mag thing.
First - have you got close to 0 ohms from inside plug caps to carbon brushes on pick-ups? With the brush, spring etc there'll often be a small resistance, few ohms maybe. But if loads of ohms show up, or 'open line', then the plug cap isn't attached correctly.
Secondly, small variation in points gap isn't the problem here I don't reckon. It affects things slightly, but as long as the gaps are somewhere close to correct and the points are squeaky clean, it should work. A good wheeze is to take an old plug, grind off the earth electrode, and stick that on the HT lead. With a good 4mm-ish gap, you should get a smart crack of a spark at kickstart speed, no problem.
Third, Swarfy's point about steel cb assemblies - the blade must not kiss the camring or it's bye-bye some or all sparks.
Fourth, a quick HT test . . . if you put a meter on the Resistance scale from the brass of the slipring with a pick-up off, and the other probe to mag body or a good earth, what do you see? Should be c 5000 ohms typically on a K2F. Open Line says a break in the winding, or that slipring-to-coil contact is absent. There should be no problem in this department . . . but you never know.
Fifth, ref possibility of timing having altered . . . If the ATD assembly hasn't moved and the teeth haven't stripped, what does the keyway on the cb backplate's male taper look like? Does it still exist and does it engage properly with the female tapered bore on the armature? If the cb is not correctly positioned, the thing will work badly, or not at all, as the internal timing will have been lost. The keys are fragile and can be wrecked by clumsy fitting of the assembly, also as a factor of age and loads of 'on-and-off'. Hard to feel with the mag on the bike if the drive is connected, but with it off the machine (or with just the ATD off so you can feel what is happening), can you see that the points start to open just after the flip points of the armature (which you should be able to feel easily)? (The key can be reclaimed using a little broach made out of, say, a bit of blade from a small reamer, if need be.)
Sixth, it's a tough one to test, but I wouldn't be totally surprised if the condenser(s) that will be in there have failed, even though the problem isn't the typical 'just when hot'. The hassle here is that you can't test the thing while it's wired to the primary winding, and it's made worse by the fact it will be potted in resin and bloody hard to get at. But if all else tests good and it's not a fuel / valve / other problem, that's maybe where you'll have to go next, unless you want to go electronic of course.
