The next tricky spot will be the leading edge of a doorway. Since you can't slide a board under the door with a U-shaped notch, break this section into two different boards. We chose to install the closet board first and then slide it back under the door trim using a pry bar.
For complicated cuts, make a drawing with dimensions so you can prevent cutting the piece backward which is a very common mistake.
Then an L-shaped board can be cut to slide in from the other side.
Tap this piece into place and then slide it under the door trim by tapping it until it joins the previous piece.