I currently have a custom icon set for one of my applications (Clover) and have it pinned to one of my taskbars.
I have my taskbar setting set to "Windows taskbar shows all windows, DisplayFusion shows relevant windows"
I have a four monitor setup.

When I open up Clover on the monitor that has the item pinned to the taskbar my custom icon shows up. Because I have the Windows taskbar showing everything, the Windows taskbar also shows the proper custom icon.

When I move my Clover window to any other monitor where there is no configuration, it ends up showing the original icon in the taskbar that is assigned to the actual EXE and not the custom icon.

I'm able to have the custom icon used if I setup the application on the other taskbars, however, I do not want the application to be pinned on those taskbars. I do want my custom icon to show. I'm also able to get the custom icon to show if I change my taskbar mode to: "All taskbars show relevant windows" and copy the shortcut to all the taskbars.

Is there anyway that I can have this app pinned to a single taskbar with a custom icon and have that custom icon show on all monitor's taskbar when the window is active on that monitor.

Attached is a screenshot as well as the troubleshooting log so you can see my settings.

To try and solve this problem, I ended up downloading ResourceHacker to actually change the icon of the actual EXE file.
http://www.howtogeek.com/75983/stupid-geek-tricks-how-to-modify-the-icon-of-an-.exe-file/

However, after doing this, the improper icon still shows up. I've removed all custom icons in my settings and the taskbar that I have set up still shows the proper icon. However, on all other monitors, the old icon is still showing even though that icon is no longer actually part of the program that is actually running anymore.

Is the icon cached somewhere to keep the taskbar snappy? If so, how can I refresh that cache of icons?