At a previous school where I worked, they adapted their system of sending updates so that all campus-wide emails were combined into one message, with a table of contents at the front. I'm not sure how they managed this-- I don't think it was completely manually. A listserv software's Digest function does this automatically, and that may have been what was used.
Sending out a single message (or, perhaps, up to 4 messages) per night with a Digest of announcements *might* be a way around the load, depending on whether the load issue is the number of separate messages (headers, etc) or just the size of the messages themselves. I suspect a digest takes up less room/bandwidth than the separate messages.
For the record, I think that we should be able to send out 2 messages, one an announcement and one a reminder; but if you can't do both, I'd rather see the campus-wide message be an announcement well ahead of time.
"Comment is free, but facts are on expenses." - Tom Stoppard