You pretty much have only three options that I know of:
1. It's not hardcoded, but PMB records the date/time stamps as a subtitle track when authoring AVCHD disks. Unfortunately, Sony didn't expose this hidden functionality for DVD authoring (a serious omission if you ask me).
2. You could capture via HDMI your clips playing back with the data overlayed. But, that's expensive (you have to get a video capture card) and annoying to do (you have to capture in realtime).
3. Your best answer is most probably a tool called DVMP Pro (google it). It support overlaying metadata with lots of controls, or even extracting it in a csv file that you could then convert into a subtitle track via another tool. Then you just need to find a codec or an NLE that will load that file.