Catalysis of the reaction: 1-deoxy-D-xylulose 5-phosphate + 2-iminoacetate + thiocarboxy-adenylate-[sulfur-carrier protein ThiS] = 2-[(2R,5Z)-2-carboxy-4-methylthiazol-5(2H)-ylidene]ethyl phosphate + [sulfur-carrier protein ThiS] + 2 H2O.