If Jupiter and Saturn were considered stars, which of their moons would qualify as planets by 'clearing the neighbourhood'?
I've noted before that the IAU naming critera are guidelines rather than laws of nature.  If applied to Jupiter's moons the four Galilean satellites would probably be &quot;planets&quot; (they don't share their orbits with anything else of comparable size and are large enought to be in hydrostatic equilibrium)  There is a mean-motion resonance 4:2:1 between them but this is a more or less symmetric relationship without one body dominating another.
The other moons are tiny by comparison.  There are 4 major bodies orbiting Jupiter.
For Saturn, Titan certainly dominates its orbit (Hyperion is much smaller.)  Dione and Rhea also seem to have a value of mu that are over 100 (though determining the value is tricky because not all moons and moonlets have been discovered) Enceladus and Tethys and Iapetus also seem to qualify,  As you note, Mimas is too small and borderline spherical. The other moons are just so much shrapnel by comparison.
So there would probably be the six pre-1800 moons, minus Mimas.
It is possible that the rules might be bent, the Rings are no permanent features, so they might be ignored for the sake of planetary determination. Remember the rules exist to serve us.  Humans make the rules. Some can be bent, some broken.