If I had a week where I could work on anything I wanted, I know what I would do. I would wrestle a piece of modest hardware away from someone, and I would install, configure, and integrate Zimbra. Finally, a webmail and online calendaring app worth using! No, seriously. I am not one to shell out praise for software. But, go head, try out the demo. After you are amazed, check out the Flash demonstration.
I wish I could hard-link to it, but in the flash demonstration, there is a section on integrating 3rd party web applications into Zimbra — looked very promising.