So hearing the video, I highly doubt its "mechanical" in nature. It sounds like an exhaust leak. The fact it only does it when running but not when cranking (with the coil wire off) is the clue. Also, this was probably caused when the engine backfired. Ensure the header gaskets (including the collectors) aren't blown. You could also idle the engine and pull the plug wires off one by one. The noise should quite down to the "cranking level with the coil wire off" level when you find it.
If you can eliminate the exhaust theory and prove me wrong, I would change my mind and think about something in a cylinder. First thing would be a compression test. If you find a dead cylinder, I'd suspect a broken ring land and damaged valve. That "whooshing" sound is indicative of air leaking past the valve seat. If these heads have ever had valve seats installed, that is another possibility too. I had a late model work truck that dropped a valve seat and it sounded very much like your video.
Another possiblity-Is this an auto transmission? If so, the backfire may have cracked the flexplate. I have had a cracked flexplate and it also sounded similar to that.
Are you sure you're not missing a 10mm socket?