You need to call up Sony, Samsung and ask them directly. I know what you are asking but today you have to run the video out the HDMI or analog connection to get the overlay or run it through software.
The recorded files do not have the time on the video so this means outside of surveillance devices you shouldn't see this in the consumer or prosumer products.
You have claimed that others have these models and my bet is that those are discontinued. My bet is you'll be upset over the offerings today since not one burns the timecode into the video itself. It's in the timecode data area.
My advice is to call each maker soon. And after it's all done, come on back to discuss how we can hardsub the timecode onto the video.
My state requires a date/time stamp including seconds. What camcorder do you use for legal depositions? Does it burn in a timestamp that is in hh/mm/ss format?
Not looking for a hack, or software solution, or vague info. Looking for brand and model number of a pro camcorder now on the market that will do what I need.