One thing you might be able to leverage is the Featured Content widget. It's similar to sticky threads in that administrators of a space can say "Feature this content" and then a widget on the overview page will show featured content only. This requires you to use threads or documents, rather than announcements, but it's one way to solve the problem.
Another option is to use the View Document widget, which will display the full contents of a Document on the Overview page. You could use the document to summarize the latest announcements or simply make people aware that there are multiple announcements. Alternatively, if you don't want a document, you could simply use the Formatted Text Widget, which will give you an RTE to post content on the overview page.
Finally, in version 5.0, we are planning on creating a social inbox as part of the "What Matters" initiative. As part of this work, People will be able to follow places they are interested in, and if an announcement is posted in that place, it will appear in that users inbox as a read tracked item that they can view and dismiss. This should help to ensure that everyone interested in a space, project, or group will see all announcements posted to those places without having to navigate to each and check.
Excellent stuff Nick. Thank you! I should have mentioned that we are running on Clearspace at the moment but will be upgrading to SBS. I've been emailing Joe Lokis for 2 days to discuss upgrade options but have not heard back from him yet. I'll call today. Thanks!
PS: When is 5.0 slated for release?