We got stuck in a similar issue with our schools. The cafetorium is scheduled for lunch at that time and doesn't have cable anyway. It also serves two different schools that are linked by the cafetorium. The only places that cable exists are in the libraries that can only sit about 30-50 kids each (grade level sizes are 130-150 per grade level and we are talking about 6 grade levels). Some grades wanted to watch live while others wanted to watch later in the day. I solved it with the new web server I was setting up. I am going to stream CSPAN over our network to classrooms with projectors.
I am using Quicktime Broadcaster along with QTSS (This is what we're using. You might find an alternative that fits your system better). Quicktime Broadcaster will also record the event at the same time and we will have it available shortly afterwards as a streaming video.
I chose CSPAN specifically because of their rebroadcasting rules.
This allows us not only to broadcast it but also rebroadcast it for the high school the following week for class use since they have mid terms during the event.
The sad thing is that these schools were going to have cable installed in each classroom but the school board at the time worried about students/teachers watching tv all day. On top of that, the newly negotiated cable franchisee they signed just last year included wording that the school/town needed to pay for any new cable installation beyond the one they already have installed. Since we just found out that are state isn't giving $421,000 of the expected subsidy we budgeted in for this fiscal school year, we are sort of in a budget freeze. Work with what you got!