A more strategic approach would be to push through Outcast space.
Strategically appropriate, but would wreck the gameplay of the Outcasts, as well as the factions who make money off the Cardi trade.
And as Aet said, it would cause all Sirius to set aside their differences and ally against Gallia.
That being said, perhaps Gallia should fund a group like the Hogosha to bolster their efforts to hamper gas mining operations? Gallia could also have some kind of group equivalent to Privateers to sneak out and do some damage.
Gallia doesnt have to completely stop the gas flowing - a low-level, longer term operation could be just as damaging to the Sirius economy, without any real political backlash against Gallia.