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Emerging non-volatile main memory (NVMM) is rapidly being integrated into computer systems. However, NVMM is vulnerable to potential data remanence and replay attacks. Established security models including split counter mode encryption and Bonsai Merkle tree (BMT) authentication have been introduced against such data integrity attacks. However, these security methods are not readily compatible with NVMM. Recent works on secure NVMM pointed out the need for data and its metadata, including the counter, the message authentication code (MAC), and the BMT to be persisted atomically. However, memory persistency models have been overlooked for secure NVMM, which is essential for crash recoverability. In this work, we analyze the invariants that need to be ensured in order to support crash recovery for secure NVMM. We highlight that prior research has substantially under-estimated the cost of BMT persistence and propose several optimization techniques to reduce the overhead of atomically persisting updates to BMTs. The optimizations proposed explore the use of pipelining, out-of-order writes, and update coalescing while conforming to strict or epoch persistency models respectively. We evaluate our work and show that our proposed optimizations significantly reduce the performance overhead of secure NVMM with crash recoverability.