I have had quite a bit of interest in being able to do this over the years and so have started to develop a small experimental open-source geospatial analysis library, called GoSpatial, with this exact purpose in mind. There aren't many tools in GoSpatial yet, but there is a breaching tool (BreachDepressions) that is based on the tool in Whitebox GAT that you are referring to. I have recently written a paper that describes how this tool works in detail,
Lindsay JB. In Press. Efficient hybrid breaching-filling sink removal methods for flow path enforcement in digital elevation models. Hydrological Processes. DOI: 10.1002/hyp.10648
which you can download from this site:
I think you'll find that this breaching tool satisfies your need for an improved method for sink removal and flow enforcement. The tool takes a number of input DEM raster formats, including the ArcGIS binary raster (.flt and .hdr files) and GeoTIFF files, and will also write the modified DEM in these same formats. There is also a short description of how you can call GoSpatial tools from a Python script at the library's GitHub repository. The example shows how to call the FillDepressions tool, but the idea is the same for the BreachDepressions tool it just uses different parameters. If you read the paper, you'll find that I am strongly discouraging people from filling their depressions when breaching (and breach-first hybrid methods) provides a far better solution for flow enforcement under most conditions. So you might see the irony in the fact that I used the FillDepressions tool in the example Python script on the site. Anyhow, if you need help with it or run into any problems with the library, please let me know.
Significant progress has been made recently that has resulted in a need to update the original answer. It is now possible to use Python to call many of the geoprocessing tools in Whitebox GAT using the new WhiteboxTools library. While WhiteboxTools does not currently allow users to access all 400+ Whitebox GAT tools, approximately 300 of the original tools have been ported over to this new stand-alone geoprocessing library. The following is an example of how to use Python to call a tool:
# import WhiteboxTools class from whitebox_tools.py script
from whitebox_tools import WhiteboxTools
wbt = WhiteboxTools()
# set the working directory
wbt.work_dir = "/path/to/data/"
# run a 9 x 9 mean filter
wbt.mean_filter("input_file.tif", "output_file.tif", 9, 9)
More detailed examples of using Python scripting to interact with WhiteboxTools can be found in the user manual.