I started working on the track early this morning. I came up with a method for laying down the braid through the underpass. After I cut the section of braid to be replaced to the proper length, I suspended the middle portion over the track surface between a small anvil and a board.

I used blue painters tape to mark out a portion of the braid recess in the underpass to apply glue to. I also marked that section out with blue tape on the new braid, so the corresponding portion of the new braid could also have glue applied. For those unaware the proper procedure for applying contact cement is to apply the cement on both surfaces, let them dry, and then bond the two surfaces together. After the braid was secured with blue tape to the anvil and then board, I slid the anvil, braid, and board out from the underpass. With the braid in the open I could easily apply the contact cement to the top surface of the braid.

While the braid was still outside the underpass I also applied contact cement to the braid recess in the underpass area. Once both surfaces had cement applied I slid the anvil, braid, and board back into the underpass, being careful not to let the braid contact the track surface or braid recess.
This is the cut down brush I used to apply the contact cement in the limited access of the underpass area.
