I liked this episode, but either I missed something or Issac made a mistake.
He seemed to imply that something like orbital rings ("active support") could compress the planet Jupiter, to increase its fusion rate. However the only inward force orbital rings exert is their weight. In other words, the only way to compress Jupiter with a shell would be if the shell were very massive, more massive than whatever mass is already holding Jupiter's atmosphere down. In the end you might even need to add the mass of a conventional star to make it work.
Maybe an alternative is to dump small black holes into the gas giant? Hydrogen will compress to event-horizon densities around each black hole and fuse, emitting lots of energy such as comes from an accretion disk.
The only challenge would be to keep the black holes from merging into one big singularity in the center. Which makes me wonder, would a black hole have any air drag in Jupiter's atmosphere? Or would a swarm of black holes just orbit around the core, sucking up hydrogen and emitting light for centuries?