OK. So, I installed the Brightspark capacitor, FINALLY got the points set to .012 and set the plug gap to .015, and also cleaned up the pick up brushes. Got the bike to idle again, but it's backfiring out of the carb and still dies when I hit the throttle. I'm ordering new brushes and a contact set with a new armature from DomiRacer tomorrow and see if that makes a difference. I also found a guy locally who sells vintage British bike parts and he's going to sell me a brand new Amal 930 concentric carb, jetted to my likings, for $189+tax.
Though, not running quite right yet, I have made some progress on the bike. I fabricated a custom seat with 2" memory foam, installed a side mount plate bracket with a '33 Ford tail light, and completely rewired the bike and converted it to a 12V system with a Sparx battery eliminator. I'm slowly getting it ready for the road and trying to upgrade as much as possible to more modern parts. Basically all I have left to do is get this thing running right. And with all of your guy's help, SEVERAL hours of Google research, and some Ebay purchases, I'm very close to being done.