This paper proposes ElastiCast, a novel Bluetooth Low Energy (BLE) broadcast mode that reduces the neighbor discovery latency in offline finding networks (OFNs). ElastiCast adapts the broadcast mode of the lost devices to the scan modes of the finder devices, considering their diversity. We start with an overview of OFNs, followed by a detailed analysis of the issues and challenges of existing solutions, which motivates the design of ElastiCast. Then we provide Blender, a simulator that models the neighbor discovery behavior of different broadcasters and scanners. By adopting Blender, ElastiCast can be implemented with three components: Local Optima Estimation, Common Interest Extraction, and Interval Multiplexing, in which we capture the key features of BLE neighbor discovery and globally optimize the broadcast mode interacting with diverse scan modes. Experimental evaluation results and commercial product deployment experience demonstrate that ElastiCast is effective in achieving stable and bounded neighbor discovery latency within the power budget.