1000s of people means that you are going to have to consider performance and the impact on your service provider.
You can scale your actual processing by using multiple machines to run the service, but I think you need to design at the whole system level, and assuming other villages will do the same. That should mean discussing this with service providers, and, as I assume this is an area with mainly mobile infrastructure, the mobile operator. Are you sure that FM broadcasting is not a better choice?
Both IP networks and telephone networks are designed on the basis of relatively few user actively using them at one time. If the dominant IP traffic in your country is web browsing, the network will not be designed to cope with most of a village listening to a media stream (even more so if it is sized just for email). If the dominant use is video on demand, you will probably have no problem, but, otherwise you may find that you become the dominant traffic source.
(Streaming media has always been a bad fit for IP, as it is a packet network, and packet networks are best when delivery delay is not particularly important, and traffic is very variable from any one source.)
The most efficient way of doing this in Asterisk is likely to be to use conferences. The most efficient way of doing this over IP is using multicast, but I don’t think Asterisk supports that, and consumer grade IP services also won’t support it.