S-adenosyl-L-methionine-dependent protein methyltransferase that trimethylates the N-terminal glycine 'Gly-2' of elongation factor 1-alpha, before also catalyzing the mono- and dimethylation of 'Lys-3'. Belongs to the class I-like SAM-binding methyltransferase superfamily. EFM7 family. Extended N-terminus.