Quite unsurprisingly, the Star Gods know a lot about making shields, and the shields they're using on their own ships are quite on a different level than the cheap knockoffs the Church is tinkering with. Not only are Star God shields more efficient, they have devised a number of support technologies to further enhance their potency. Most of the physics involved is far too arcane to understand, much less learned from an interrogation, but I think we have gained the understanding of at least one useful bit; with enough technological base of our own, we'll be able to devise shield recharging systems small enough to fit our miniature craft.