Create a local or account folder and add an action to actually move the message out of the inbox as part of the filter processing.

Thanks Matt Sounds good! I have applied that to my filters (assuming the move should be after the forward). I await relevant emails to test this. Given that it will work, that is very good. There is the downside that I have to look in two folders for new mail - the inbox and specially created folder, given that I want to see it, and have it passed on automatically. But that is still way better than where I am now!

You could create a saved search (ctrl+Shift+F) to locate unread mail in both folders and simply use that instead of the inbox. It will show up in the folder pane as a folder is saved. The downside is it is not updated until you select it.