Only take the time to read this post if you’re interested in how I came to my conclusions, about one post before the actual solution was posted. I suggest this with all humility, a few may find this helpful, enhancing or notice different trouble clearing ways.
I just started reading this posts today. This may sound like a 20-20 hind sight thing but it's really not. This is what I was learning and thinking as I read the posts in progression, post #1 toward the fix. Very nice video particularly the audio. On the failure to start times, I detected what seemed like a shorter cranking time than slightly longer cranking during a successful start time. Now thinking for a reason, the starter is dropping off early.
Then the P068a DTC (Diagnostic Trouble Code) information was posted. I looked up the P068a code. The site I happened upon talked about what happens, if the PCM (Powertrain Control Module) detected low voltage from a relay in the starting process. The PCM monitor’s that relay, if and when a low voltage is detected, it shuts down the starting process. Now we know why it ended before it started.
Now I am thinking, (did you see the smoke?) some of the members who are suggesting low voltage as they posted battery related suggestions but the battery had been posted as being good. ?? With all those thoughts in mind, I now see the post, the passenger door only, no longer unlocks or locks from the outside door handle, in response to a posted question. That locking comment, also tells me your battery voltage was low and it all clicks together. Time to go back and re-check the battery first and then if necessary start looking for the relay with low voltage feeding back to the PCM.
Too bad you can't watch the battery voltage in the instrument cluster as its cranking. I had also noted the video the Instrument Cluster Panel was going dark as the engine was cranked, I don't remember my F-150 doing that. If it doesn't normally do that, that certainly an indication of a drop in voltage (battery) or a bit of corrosion at the battery terminal. Now I know for certain, the battery voltage must be dropping off during the starting process. If we had a volt meter we would see the battery voltage low all the time. Why do I have those thoughts? My truck’s, parasitic currents discharge the battery, bringing its voltage down, after days of sitting, the first thing I see happen, the passenger door's outside door handle lock cease to function, (lock or un-lock). The driver side always works. I posted on another forum commenting about my Passenger door lock and battery findings and two other members, posted their trucks do the exact same thing. Long story short I put a battery charger on it, bringing the battery back to full charge, voltage back up. All cleared and the truck never move out of the driveway.