There appear to be several options for sub-second timestamp encoding. As it turns out, it appears to be possible to submit centiseconds in the GPS string, the camera appears capable of reporting GPS time to this accuracy, and the camera can report its time of the image (in camera time) to the centisecond. (Details of this and other relevant metadata, and GPS commands, are appended below.)
With this knowledge, the best option appears to be as follows. Steps 1 and 3 are safeguards to make life easier if, say, the camera clock drifts badly, or our GPS time resets during the mission. But they shouldn't actually be necessary.
Depending on the analysis for step 4.1, either a fixed offset from GPS time can be used on future missions, or an additional timestamp calibration can be determined for each set of images so that the camera time can be used to more precisely offset the GPS time.
There is an Exif field within the picture metadata that captures centiseconds for each picture. (This number is associated with the camera time, not the GPS time.)
The GPS Timestamp field is a triplet of ratios; the first two denominators are 1, so hours and minutes are integers; the seconds demoniator is 100. So it appears centiseconds in the GPS string may be entered into the metadata of the picture.
The GPS MapDatum field is a string of 9 bytes (10 including terminator). This is sent with a 'Garmin proprietary' command; not clear if camera processes that.
Latitude and longitude have a similar structure, but are assigned according to the format of the input. (For example, if the input minutes of latitude is 59.296, the denominator might be 1000, and the numerator 59296.) Certainly between them we could get a representation for centisecond-level time encoded. Less desirable because metadata is 'wrong' in the raw images, but this can be fixed in processed images.
There is a user comment field in the Exif metadata area. The camera may support entering comments via one of its command interfaces (PC or USB), but I didn't check this out.
The GPS format is NMEA 0183. It provides for a GPS/Transit data set that supports centiseconds in the time field.
Latitude and longitude do not appear to have sufficient resolution for a full timestamp with centiseconds, though the stored values support it.
RMC = Recommended Minimum Specific GPS/TRANSIT Data
$GPRMC,hhmmss.ss,A,llll.ll,a,yyyyy.yy,a,x.x,x.x,ddmmyy,x.x,a*hh
1 = UTC of position fix
2 = Data status (V=navigation receiver warning)
3 = Latitude of fix
4 = N or S
5 = Longitude of fix
6 = E or W
7 = Speed over ground in knots
8 = Track made good in degrees True
9 = UT date
10 = Magnetic variation degrees (Easterly var. subtracts from true course)
11 = E or W
12 = Checksum
This is nominally a proprietary Garmin format. But it's possible the camera transfers it.
$PGRMM,NAD27 Canada*2F
Currently active horizontal datum