S-adenosyl-L-methionine-dependent 2′-O-ribose methyltransferase that catalyzes the formation of 2′-O-methylguanosine at position 1370 (Gm1370) in the 16S mitochondrial large subunit ribosomal RNA (mtLSU rRNA), a conserved modification in the peptidyl transferase domain of the mtLSU rRNA.