Hey Jay - Unfortunately, changing out those icons is easier said than done. I initially went down the route of having custom uploaded icons as the only option, but consistency and appearance suffered, so I settled on Maki icons - they're easy, flexible, and lightweight. If you're set on the custom route, and if you're comfortable with some pretty dense coding, I can tell you where you'll need to customize:
1) UI script 'flexible_mapper_js': Specifically, there's a function called 'getMarkerIcon'. This takes the icon as listed on the Container Style and fetches it from Maki for display. You might be able to get away with just editing this script and passing back your custom icons based on some attribute of the Container or Style.
2) Script Include 'FlexibleMapperHelper': This is where the maps are built up server-side and sent over to the client. There's a labeled section in the 'loadCargo' function where the Container Styles are packaged up for shipment. Not sure if it'll be necessary, but you could add some additional data here to be parsed at the client (by the UI Script above).
There may be a simple way to accomplish what you need, but it isn't immediately apparent. When you start digging, you'll see that those scripts can get fairly involved.
Best of luck - I love the look that you're after - let us know if you are able to put it together!