Aeropress Travel Filter Holder

I love my Aeropress(es). I have 3 of them. What I don't like about the Aeropress is when I travel, I have this bag of stuff and it is easy to leave a piece behind. I would like it to assemble into a single unit for travel, as much as possible. For example, if the screen thing would have been 1mm deeper, it could attach to the press. And then there are the filters... I bet everybody has a ziplock baggie with a bunch of filters in it.

I attempt to fix both of those issues with this thing.