Thanks, John.
For the first, you are right. Although the comparison between SPP 5 jpg and SPP 6 shows that the difference is the presence of IPTC timestamp, it seems that LR 5 does recognize a photo only with an Exif timestamp from another camera.
It means that some other part is wrong with SPP 6.0.2 jpgs.
As for [Edit Capture Time], I meant a batch correction. [Adjust to a specified date and time] only works for a single photo, I guess.
"Shift by set number of hours" is good for time zone adjust, but sometimes one would notice that the camera time is wrong.
Other photo edit tools, for example, PlayMemories Home can shift multiple timestamps in minutes.