Lightroom's video metadata leaves a lot to be desired, though it has gotten a littler better. You can turn on writing the date back to the file in Catalog Settings (EXIF in the Metadata tab), though I've not tried it for video. Just remember to switch it back.
Any suggestions on how I can force the Date Captured metadata into a format readable by LR?
As Sean mentioned, LR's support for video metadata is incomplete and buggy.
For many video files, LR doesn't read the metadata at all. For these files, it shows the date/time of import for Capture Date/Time in the Metadata panel, and it shows the operating system's file last-modified date/time under the thumbnail in grid view: Lightroom: Still inconsistent capture date/time for videos
If you want to beat your head against the wall and try to see if there is a metadata field that LR will read, I suggest using the free Exiftool to examine a file whose capture time it does read and use Exiftool to modify the video. (But beware that the file last-modified date/time is often the same as the capture time in the metadata, and LR may be using the last-modified date/time.)
You can turn on writing the date back to the file in Catalog Settings
Unfortunately, LR doesn't ever write metadata back to video files: Lightroom: Metadata applied to videos in Lightroom isn't available in other applications
If you care about your video metadata, you could use the Video Asset Management plugin or the Any File plugin. These plugins import a JPEG "proxy" for the video rather than video itself, and metadata changes get written by LR back to the JPEG. So if you ever want to take your video and metadata into some other program, you're assured its written in industry-standard form in the JPEGs. (And a tool like Exiftool can easily extract it.)
Cheers for that johnrellis! Like I said, I hadn't tested it. I did know the support was sketchy, but at least they added reading from sidecar files that contains metadata. While I'm starting to do more video, I'm not really managing my final exports in Lightroom-no particular reason, so I haven't been up to speed on exactly what the current state of play is.