Catalyzes the methylation of 5-carboxymethoxyuridine (cmo5U) to form 5-methoxycarbonylmethoxyuridine (mcmo5U) at position 34 in tRNAs. 5-carboxymethoxyuridine(34) in tRNA + S-adenosyl-L-methionine = 5-methoxycarbonylmethoxyuridine(34) in tRNA + S-adenosyl-L-homocysteine Homodimer. Belongs to the class I-like SAM-binding methyltransferase superfamily. CmoM family.