To my ear the engine changed tone slightly, twice before it quit.
Stop was sudden, seems more like a switch than fuel starvation.
Have you watched the tachometer while it is running?
Is the RPM steady or fluctuating, does it decrease in steps before stopping?
I've also watched it a couple of times now. I don't pick up a massive change in engine note but the idle sounds quite fast compared to my car so it's harder to pick out. I'd need to see the rev counter I think.
I must admit I was strongly on the fuel starvation option but I'd also agree that the cut-out was much quicker than I expected from running out of fuel, it's more like the ignition was turned off. With that in mind I think I'd also revisit the electrics and make 100% sure that there's a strong spark immediately after the engine cuts out because that's simpler than rebuilding the carbs.
I use inline testers such as the one in the attachment, very simple to plug in and check there's a good spark. You might have a spark that's simply not strong enough to ignite under compression but good enough to flash on a plug in the air.
Would it be too difficult to just return the ignition system to stock as a test?
That's got to be an option, the old fashioned CB points, condenser & coil might not be desirable from a long term maintenance viewpoint but it is very simple and easy to install.
Brian