Yeah,
$150 is pretty steep for a set of points!
One thing you might try, if the point faces you have aren't pitted and have good contact, would be to use a quality 2 part epoxy to build up the cam rider a bit or attach a phenolic tip to the stub. Might work for a while.
BTW...gap is 0.012" to "0.016".
It used to be that if you went to a Napa store on a Wednesday (slow day) and asked nice, ( I wouldn't use the phrase "I summon" as you did here) someone could try to match up the points you have from inventory. But I'm not sure they even stock breaker points anymore these days. But I bet Echlin still makes them for old cars.
The "lighting" (primary) coil resistance is listed as 2.0 ohms
The condenser capacitor value as 0.24 mfd.
There is a hand written note in a shop manual I bought used that says a Borg Warner G610 capacitor will fit but I have never tried one so take that with a grain of salt.
I don't know what the start volts should be for the primary coil. It is rpm dependent and will vary. I believe it can get up well over 50 volts ac while running but not positive. Haven't worked on one of these in years and no notes on that.
The permanent magnets in the flywheel can de-laminate and weaken volts. Rust building up on the coil ends and magnets can weaken volts as well. All you can do there is remove the flywheel and inspect, clean or replace.
You are correct that the charging system has no bearing on the ignition system or oil lamp operation.
But, you can get the coil rewound if you're interested in restoration so don't throw it away or pick at it. A rewinder will need it for the core and to count the turns plus wire size.
Hope this helps some.
Good luck.