Catalyzes the cyclization of GTP to (8S)-3',8-cyclo-7,8-dihydroguanosine 5'-triphosphate. AH2 + GTP + S-adenosyl-L-methionine = (8S)-3',8-cyclo-7,8-dihydroguanosine 5'-triphosphate + 5'-deoxyadenosine + A + H(+) + L-methionine Binds 2 [4Fe-4S] clusters. Binds 1 [4Fe-4S] cluster coordinated with 3 cysteines and an exchangeable S-adenosyl-L-methionine and 1 [4Fe-4S] cluster coordinated with 3 cysteines and the GTP-derived substrate. Cofactor biosynthesis; molybdopterin biosynthesis. Belongs to the radical SAM superfamily. MoaA family.