LSM compaction space amplification

An LSM-based key-value store backing a metadata service is suffering: disk usage is 2.3x the live dataset, read p99 has crept to 40ms, and deletes don't seem to free space for days. Workload is heavy overwrites of the same keys (config/state that updates frequently) plus a steady stream of deletes (TTL expiry), uniform key distribution, dataset ~3TB. Design a compaction strategy (and the surrounding knobs) to fix space amplification, restore read latency, and make deletes reclaim space promptly. Explain the trade-offs versus the alternative strategy.