Ignition woes

Dan stated it perfectly. You have erratic connections in the bulkhead connector. If you are sure they are all clean now, leave the engine side latched, crawl under the dash and push each terminal in with needle-nose pliers. They are simple spade connectors ("57 terminals" or "Packard 57") and yours aren't latching properly in the bulkhead so they push back when you plug the connectors on.

I had your exact same original problem when I re-wired my car and thought I could skip the brown wire (bypass) since I plan to eliminate the ballast later anyway. Much to my surprise, the IGN wire doesn't get +12V when in the cranking position on the key switch. I found it would only start as I released the key. Your last problem is the same as a broken ballast resistor or a bad IGN connection.

Also check your key switch. My 64 Valiant cut out 10 miles after I bought it, so I hot-wired it to get home. I found the key switch was missing the factory connector and had multiple spade connectors that were coming loose. One of many wiring hacks I had to fix on my cars.