Hi Robert,
I believe that the "Project" Dropdown is poorly named. It really should be considered a "Team" dropdown, at least, that is how we approach it.
So, the "Project Dropdown" would look more like
Group of teams 1
Team 1
Team 2
Group of teams 2
Team A
Team B
Then, projects come through as Portfolio Items/Initiatives. Under those are Features, (which may be your epics?) However you can always have EPIC stories, that are parents to others stories.
There is a milestone feature that you can setup for actual releases, and these work for all the items that are children. So in the above example if Group Of Teams 2 has a Milestone Release for March 1, then stories can be assigned to that milestone as they get tested.
You can also create a RELEASE, these are more along the lines of "Here is what we think the release will look like", So perhaps in planning sessions you would assign 30 stories to a release on monday, and the next wednesday only 20 of those are really going, since that is all that made it through test. So those 20 get the MILESTONE attached on the date of release, and the other 10 stories end up in RELEASE2, or dropped all together.
This is the way we do it, you can alleviate the iteration issue, by breaking up your teams into groups, so in the example above instead of Group of Teams 2, name it Teams on 3 week sprints. You can create the iteration at the Group level, and allow it to flow down to the kids.
As I type this, I realize, this is alot of information And its drastically different than what you have setup now. Just thought it would help to see how others get through some of your stated concerns.
Good luck,
Tom