Actually I think it would work better as a new feature. The related issues are a way to link two different issues together, but in this case the need is to have an extra layer between projects and issues. Actually, creating Sub-Issues might work better; that way you could add sub-issues to existing issues to break them down into smaller tasks.
For example: If the issue is to correct a bug. Then you could break down the issue into sub-issues and you could assign each one of those sub-issues to different people: Fix Bug, Test Bug, and Document changes.
This feature would also be useful in cases in which the issue requires the work from different people playing a different role in the organization. For example: If there's a need to create a new feature and a db guy is needed as well as a developer. Then you could create a sub-issue for the db guy to take care of the database stuff (new table(s), new stored procedures, etc) and another sub-issue for the developer to create the programming part of the new feature.
Anyway, I hope that helps to illustrate what I had in mind. Once again, thanks so much for such a great system.