How can I update a system application without re-installing the OS?
As long as you have the release key (or whatever key you use) used sign the app in the /system you could just quickly side-load your application:

adb install -r bin/my-signed-app.apk


Note the '-r' option.

This will update the application, but not remove/update the apk file in /system or clear the user's data. 

You might have to clear the data first due to database schema changes:

adb shell pm clear my.app.package


You could then go and manually remove this 'update' via the app settings Activity.