Minecraft – How to reverse the redstone door so it starts in close position

If you watch at about 2:50, you can see most of the left half of the circuit. The part for the stairs looks like it isn't shown very well but that is less important timing wise. Watch carefully over and over and see if you can replicate it this way. It looks like the repeaters for the middle activate and deactivate immediately. So the order (from a circuit standpoint) for both directions is M, L+R. This works for closing because the middle repeaters don't have anything to activate until the blocks are pushed into the middle. When opening, they will retract the middle immediately.

Breaking it down:

Opening

1. Middle repeaters deactivate (middle pistons retract)
2. Delay
3. Left and Right redstones deactivate (left and right pistons retract)

Closing

1. Middle repeaters activate (nothing happens because the middle pistons are not in position)
2. Delay
3. Left and Right redstones activate (left and right pistons extend)
4. Now the middle pistons have been pushed into position and are activated by the middle repeaters

As far as I understand your question, you have trouble with the track going trough the door...

Here is a screenshot of my setup, first you switch over to the new track, then you go trough the 'door', but by going down under the door block the track doesnt break and just creates a slope whenever the door is open, this would work in both directions.

Also as often happens with these timed things, the doors or track switcher might not stay open long enough, here is a way to lengthen that. (This is my own design, not all that compact, but the only thing that makes sense and works for me)