I want to plot mileposts on a map every 100 miles along the coastline. An example is shown in the figure below:

It is easy to plot the coastlines using Cartopy, but how to determine the locations of these mileposts and show them on a map? It would be better if the coastlines between the points were colored.
You can use Shapely's interpolate method to figure out the location of the mileposts. However, the tricky part of this is getting a singlepart linestring for the coastline. I messed around with a few coastline shapefiles that I downloaded, but due to the complexity and distance, getting a nice singlepart linestring was not a simple task. Therefore, I chose to digitize my own for this example (digitize.shp).
EDIT:
Here is a replacement for "digitize.shp" for a full working example. You can use gpd's to_file() if you want to save cl_gdf to a shapefile.