I'm assuming they don't already offer you Exchange Web Access on that server? That would solve a couple of the issues, probably everything except the iPhone. But that would be too easy.
It might even work on the iPhone but I doubt it. The ideal solution for the iPhone is something that works within its version of Safari rather than syncing.
I dunno about the connections with Gmail Calendar, but Google does pay special attention to iPhone so that could be a good bet.
This is overkill, but at work we use collaboration app called Zimbra. The operation of this server to Outlook mimics an Exchange sever, syncing up mail, calendar, etc, and you can find an online provider that would sell you an account with those capabilities. (Some of them may become part of Yahoo since Yahoo now owns Zimbra.) But, since you're only looking for calendar, this is way overkill and maybe wouldn't really achieve what you want anyway. It does also have an iPhone-specific client, though.
Seems to me unless you can get web access to the Exchange server you are going to end up duplicating your efforts one way or another. Having the info residing in two servers, say it's the UCSF server and Gmail calendar, just seems like it's asking to get messy. Although, I am assuming it is important for your calendar info to be in a group calendar on the UCSF server. If that is not the case, then you could move all of your calendar info to something different and not have this overlap problem. Whether you can get Outlook to behave nicely with this setup is another matter.
It seems to do best when everything is combined in one.
Sorry, might be rambling and not much help, but just in case.....