...they by-pass a solid design stage and whip out the agile card. It allows them to get onto the fun parts straight away. Of course, it all turns to custard. Good design is a combination of education, and experience. In the end some perople just never get it.
You should get with the times. Agile is so out. Kanban lets you get into the fun parts with even less design.
Why don't you give Agilefant 2.0 alpha a try?
It's a FOSS tool designed to solve just the problem you have and it has most of the features you need, except file attachments, which aren't there (at least just yet). Currently Agilefant lacks some of the customization options commercial software like VersionOne or Rally have, but many of our users have been quite happy with the current functionality.
Agilefant handles multiple product, projects and iterations simultaneously with ease. In addition to normal backlog lists, it has a personal job queue for each user so you can see what you were planning to do next. If you enter your effort estimates for tasks, Agilefant will calculate how much work on average you have planned for the few next weeks.
Agilefant runs on Tomcat and MySQL and is really easy to install.
Disclaimer: I'm a former Agilefant developer and currently working on a project very close to Agilefant development.
Do not simplify the design of a program if a way can be found to make it complex and wonderful.