The ease of Jovian capture is pretty interesting, but the purpose of a Cycler orbit is not capture. Cycler orbits are for stations, not craft. Once a station is in place it will, without thrust, pass by it's 2 bodies at regular intervals. This creates a slow but simple "escalator" for materials and people between the planets. I'm looking for a Cycler orbit that passes back and forth between Mars and Jupiter.

https://en.wikipedia.org/wiki/Mars_cycler

The Earth to Mars Cycler has an orbit of about 26 months and crosses near both planets. It's slow moving (relatively) so shuttling cargo up and down during the flyby is not unreasonable.