Catalysis of the reaction: S-adenosyl-L-methionine + 4-demethylwyosine37 in tRNAPhe = 5'-S-methyl-5'-thioadenosine + H+ + 7--4-demethylwyosine37 in tRNAPhe.
tRNA 4-demethylwyosine alpha-amino-alpha-carboxypropyltransferase activity