I'll skip over discussion of Python packaging (distutils, setuptools, pip, etc), since it sounds like you'd prefer using simple zip files or tarballs. I'll address the "pain points" you mentioned one at a time:
Template files: As long as you have 'django.template.loaders.app_directories.load_template_source' included in the TEMPLATE_LOADERS setting of your projects, you shouldn't have to worry about this one. Each of your apps can have a "templates/" subdirectory, and templates in there will be loaded just as if they were in your project-wide templates directory.
Media files: App media is a pain. For development, you can use a custom serve_media view that operates similarly to the app_directories template loader (looks for media in each app). In production, you have to either copy the files, use symbolic links, or use webserver-level aliases. There are several utility apps out there that try to smooth over this problem; I now use django-staticfiles.
Editing settings.py: No simple way around this one. For its models, template tags, management commands, etc to work, an app has to be listed in INSTALLED_APPS. What you could do is write some custom code in your settings.py that lists the contents of a certain directory and dynamically adds the packages it finds there to INSTALLED_APPS. A little bit dangerous (think carefully about who has permissions to place files in that directory, because they have the keys to your kingdom), and new files there will only be detected on a server reload, but it should work.
I think if you put together those solutions, it's possible to achieve your ideal situation: unzip to install, delete to uninstall.