after watching the videos again, here's what we know:
1: with the chain disconnected from the motorhead sprocket, the chain moves the trolley by hand in both directions freely.
2: With the chain disconnected from the motorhead, the motorhead cycles back and forth ok.
3: In the last video you posted the youtube link for, the chain that tightens up and stops is the wrong side. It's trying to pull the trolley into the garage door, which won't happen, so the chain just tightens up and stops.
4: It is definitely 180 degrees out of sync as far as the chain is concerned.
If you were to disconnect the chain off the motorhead sprocket, slide the trolley back up to the motorhead and then reconnect the chain, when you hit the button, the chain on the right side of the track as pictured in your last video should be doing the pulling and the trolley should move towards the garage door. Next time you hit the button, the chain should reverse direction and the trolley should move back towards the motorhead.
At this point, if it is working now, reconnect the door and check its travel limits in both directions. You should be pretty close and adjustments can be made with the two little white plastic screws that are marked with an arrow on each one, one pointing towards the door in the up position, and one pointing down for the door in the down position. By turning either screw in the direction of the arrow, you will either let the door travel up more, or down more, depending on which screw you turn.