Actually, at least on Windows, the Developer Tools windows are not included in the browser window group, they already have their own separate group, so having a different icon should, in theory, not be a huge problem.
Also, I am not sure (on Windows) you must have a process per taskbar button. For example, while Chrome indeed has renderer processes, the taskbar buttons you see in the Windows taskbar are not renderer processes, but browser windows and as far as I know, Chrome does not start a different process per window (not even always per tab). Each Windows task (on the taskbar, that is) can have its own icon, I believe.
I do not know about other platforms.