Order the Sony a1 at http://sdp.io/a1
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UPDATE: The Sony a1 WILL close the shutter when in silent mode, but you have to change an extra setting I didn't know about - MENU → (Shooting) → [Shutter/Silent] → [Silent Mode Settings] → Target Function settings → Shutter When Pwr Off. Set that to "Not Target", obviously. Maybe that's the default and I screwed it up?
Tony Northrup complains about his favorite camera of all time, the Sony a1, and he compares it to the Canon R5, which is also great.