Beyond Frustrated - Wont start/stay running

Sounds like the engine does not have that many miles post rebuild I doubt it is cam timing.

Most likely points / condenser, maybe you damaged the dist gear is it a plastic one?

You MUST have a good condenser.

Make sure the points are actually opening and closing AND actually switching current. To do that, put a test lamp on the coil+ and turn the key to "run". If the bulb appears nice and bright, take an alligator lead and ground coil NEG. This should cause the lamp to dim quite a bit. This shows you are getting current through the coil If the lamp appeared somewhat dim, and had no change when you grounded the coil NEG, the points are either naturally closed, or something is shorted to ground. "Bump" the engine with the alligator clip lead "off" and the lamp should brighten up

Now switch your lamp to the coil NEG terminal. You may get a lamp or not. "Bump" the engine and the lamp should go on/ off. If not, you have found the area of the problem..........either the points are not conducting when closed (lamp stays on) or the points are not opening or something shorted / grounded (lamp stays off)

Problem areas are........distributor wire shorted to ground or broken "open" inside

Points so corroded / burned they will not conduct

Points just plain out of adjustment

Bad condenser.......even the new one

Bad coil

Or a power problem........key "run" voltage not making it to coil
About that final statement... Symptom/scenario described does read like failing electrical.
The starter operates on a big direct wire but everything else operates on a separate smaller wire routed through several connections. So a good battery and good starter operation doesn't tell all.
If the little connector before the fusible link should be burned nearly in two, you could have enough current to operate the starter relay but not enough to operate everything else. Of course weak connections at ignition switch, bulkhead, and more also cause low voltage.
I had one once that jump started and idled OK but step on the brakes and the draw of those few little lamps would shut the engine down. That one was a bad battery. Same lack of sufficient voltage supplied.