Self-hosted STT better than Whisper Large V3 Turbo that matches AssemblyAI quality?

I’m already using Whisper Large V3 Turbo self-hosted, but the accuracy still isn’t where I need it. I like AssemblyAI’s quality and want something self-hosted that:

- Is clearly better than Whisper Large V3 Turbo

- Can match or get close to AssemblyAI’s transcription quality

- Runs locally (no cloud API)

Is there a self-hosted model or stack that realistically beats Whisper Large V3 and gets close to AssemblyAI? Or is AssemblyAI’s own self-hosted offering the only real option at that quality level?