According to NASA's history on the mission, Pioneer 11's goals included both investigation of the solar wind outside of the ecliptic, and a look at the polar regions of Jupiter, which appeared to have a more transparent atmosphere than the equatorial regions. A close flyby of Jupiter over either pole would unavoidably sling the spacecraft out of the ecliptic,...
The problem with sending a cubesat to Saturn is power. A cubesat isn't large enough to carry a nuclear thermal generator, and almost certainly not large enough to carry enough solar cells to power it in the outer solar system.
Consider the Juno probe to Jupiter. Its solar cells weigh 340kg, yet generate only 240W of power at Jupiter, which has ...
If the orbiting body's mass is a significant fraction of the central body's mass, the weak stability boundaries can be more dramatic.
Call the mass of the central body + orbiting body 1. Call the orbiting body's mass µ. Then the central body would have mass 1-µ.
Here are pairs arranged in order of µ
This is all about gravitational maneuvers.
They allow to obtain huge accelerations/deceleration/velocity changes almost without using any energy. More heavy moons - more opportunities for maneuvers.
General idea is that if satellite trajectory at some point goes near heavy body (one of moons), by very small early adjustments from long distance before ...
Converting my comments to provisional answer.
"Saturn's Small Inner Satellites: Clues to Their Origins" by C. Porco et al. - this article in Science is paywalled, too, but pictures from the article are accessible with captions, as well as tables.
From table there (mass and density):
mass (× 10^19 g) ρ (g/cm^-3)
Yes it is not easy, but not impossible. This answer addresses the communications issues mentioned in comments.
The MarCO cubesats actually served as communications links between a spacecraft landing on Mars and the Earth. It was a slow link, only 8 kb/s using 5 W of power, and at the time the distance was only about 0.7 AU, whereas Saturn will be 9 or 10 AU ...
Data from Cassini-Huygens are given in this table from phase 76 of Reference 1
$J_4×10^6=-939.32\pm0.98$ (observed), $-971$ (theory)
$J_6×10^6=91\pm 5$ (observed)
Saturn from Cassini-Huygens
edited by Michele Dougherty, Larry Esposito, Stamatios Krimigis. (...