mythtv (backend) + xbmc (frontend) could be a valid option. But be aware that mythtv will save it to disk even its doing live tv streaming.
Assume that the average bit rate is 0.7MB/s, then the continuous disk throughput should be at least 35MB for read + 35MB write at the same time. You will also need 4 dvb (at least in UK) cards to cover the full spectrum.
Mythtv generally is quite gentle on the resources. At home by using pentium III I can stream to at least 2-3 users at the same time. If it's not powerful enough you can always have load balancer and more hardware to increase the capacity.
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