The current document is directed to methods and systems that efficiently process and store log/event messages generated within distributed computer facilities. Various different types of initial processing steps may be applied to a stream of log/event messages received by a message-collector system or a message-ingestion-and-processing subsystem. The currently disclosed methods and systems employ additional pre-processing steps to identify the types of received log/event messages, monitor event-type-associated log/event-message-usage-delay histories, and employ time-series-analysis-based and/or neural-network-based estimation of event-type-associated log/event-message usage to efficiently store log/event-messages in low-cost and low-latency storage facilities.