I solved this in a cheaty way using a graphics program (“gimp,” free) using the color swapping to quickly change the acceptable colors to white.
For example to find the blue path I swapped Blue to White, Green to White, and Purple to White. I had to use a gradient because of the compressed image format — the colors for lines were ranged rather than pure. Once the transfer is complete, you are left with white bars where there used to be (blue, green or purple).
You can then draw a line through any white bars from beginning to end and that there’s your blue path.
Example of gradient swap.
From start to finish, in Left Right Up Down notation
R D R R U R R R U L U U U L L U L U U R R R R R D R