With the ticking, take off the rocker covers and see if any rockers have extra clearance with the valve stem. If a cam lobe is going down, that rocker will be very loose
What you guys are talking about doing is a bit outside the scope of my experience and capacity. Not sure I'm comfortable with the idea of taking my engine apart to this degree in the parking lot of my three-bedroom townhouse. That's not to say desperation won't get the better of me and force me to reconsider.If GT Drew's suggestion doesn't yield the answer, you could even have someone crank the car and watch the rockers with the covers off to see if #6's valves are moving as much as the rest. To cause a misfire at least one of them would probably not have to move much at all. I'd try to find a way to stop the car from starting (pull fuel injector fuse?) but I've never had to do this on my car.... You would not want to crank the car excessively with fuel going it as it will wash the oil off the cylinder walls and start causing wear.... Actual starting could also make a mess with oil. Hell, even cranking could, I'm not sure. I used to do this with my gen1 SBCs years ago.
Is #6 a DOD cylinder? I have no idea how these can fail, but my understanding is that they have special lifters that use oil pressure solenoids to control whether or not they open the valve. Not sure if they can fail such that DOD is permanently on for a valve (and thus not opening). But it sure sounds like you have a mechanical issue. I doubt it's the crank or cam sensors for if they failed it seems unlikely that you would consistently get a misfire code on just one cylinder. Also, I believe if the car has both crank and cam sensors, it may be able to detect a failure in one from the other and set a specific code for it (was that way on my Nissan Maxima). If the fuel injector was the problem you could swap it with another cylinder.
I really do appreciate your suggestions and guidance. One thing you haven't told me is how a possible mechanical issue can manifest as an electrical malfunction in the form of an intermittent disruption of current going to a spark plug. In my experience, moving mechanical assemblies and parts don't effect electrical systems. It's usually the other way around.
If you could please help me understand that, it would go a long way towards helping me diagnose this problem.