Periodic broadcast protocols enable the efficient streaming of highly popular media files to large numbers of concurrent clients. Most previous periodic broadcast protocols, however, assume that all clients can receive at the same rate, and also assume that available bandwidth is not time-varying. In this paper, we first develop a new periodic broadcast protocol, Optimized Heterogeneous Periodic Broadcast (OHPB), that can be optimized for a given population of clients with heterogeneous reception bandwidths and quality-of-service requirements. The OHPB protocol utilizes an optimized segment size progression determined by solving a linear optimization model that takes as input the client population characteristics and an objective function such as mean client startup delay. We then propose complementary client protocols employing work-ahead buffering of data during playback, so as to enable more uniform playback quality when the available bandwidth is time-varying.