To search for moons, I generated ephemerides using JPL's Horizons software for all named moons of Mars, Jupiter and Saturn on all nights of 2MASS operations. I uploaded these tables in Gator and did cone searches with a 60-arcsec radius against the V3 point source working database. This radius was chosen to ensure that at least one field object would be detected near the predicted position of the moon (which might not be detected). The resulting tables were then searched for matches between the ephemerides and observation dates. The findings were as follows:
Mars
No observations of Phobos or Deimos. The closest we came to getting Mars was
on 990420s while scanning about 2.6 degrees away.
Jupiter
No further observations of any moons, although Pasiphae was only one tile away on 981011s.
Saturn
No observations of any moons. The closest we came to getting Saturn was on 991222n
while scanning about 1 degree away.
Performing a search in the V3 point source list on the positions of the detected moons listed in the above web pages gives this table (no filtering) and this table (catalog selection criteria). Note that Uranus was scanned twice (the webpage above only lists the 980607s observation), and that on 980607s it appeared in two adjacent scans. Using the catalog selection criteria drops a spurious K-only detection of Uranus 1.6 arcsec away from the other detections, a glint-contaminated detection of Miranda, an H-only detection of Oberon, and a 3-band detection of Umbriel which does not have anything obviously amiss. Note also that some of the V2-detected moons of Jupiter are in scans that were not run in V3 processing.
I propose that these moon detections be flagged as part of the final catalog generation. This is an operation that needs to be discussed among those more familiar with DB operations than I. Some combination of setting mp_flag to 1, adding an entry in the mp catalog, adding a an entry for mp_key, and adding a name would seem to be necessary. At present I do not know if just providing names of the moons would be enough to identify them. Are there asteroids with some of the same names as these moons? I'd think the IAU would be smarter than that, but maybe to be on the safe side, something like appending the name with -J for Jupiter etc. would be a good idea.