If you had uploaded a sample photo to Dropbox or similar, we could have saved you many hours of work.
As you've discovered, PSE allows capture date/times with unknown (unspecified) seconds, minutes, hours, days, or months, but LR does not. The industry standards are ambiguous about unknown date/time fields (details upon request), and most programs don't implement them. Further, at least as of version 8, PSE had many bugs with unknown fields (and knowing Adobe, I very much doubt they ever fixed these bugs). LR gets confused by them. Windows File Explorer also doesn't follow the industry standards.
A few people have long requested that LR implement unknown date/time fields -- see this feature request in the official Adobe feedback forum: Lightroom ignores partial dates imported from Elements | Photoshop Family Customer Community . You could add your me-too vote and detailed opinion to that feature request, but given how old it is and the ambiguous industry standards, I doubt that Adobe will pay much attention. We could at least hope that LR did a better job of converting PSE catalogs containing dates with unknown fields, but again Adobe has shown little interest in fixing the numerous problems with PSE catalog conversion.
I use the convention that an unknown time is represented as "00:00:00", an unknown day as "1", and an unknown month as "1". So if you just knew the year, it would be represented as "1943:01:01 00:00:00". Another person has mentioned he uses a similar convention but also adds a special keyword indicating the date has unknown fields. This approach has obvious ambiguities, but it's better than nothing.
You could use the free ExifTool to find all photos with unknown date/time fields and then fill them in with 0, but ExifTool has a steep learning curve, so unless you're very experienced with scripting command-line tools, I recommend against trying it.