The name of the illustrator for Golden Time is spelt with what seems to be the accepted spelling in the manga world: Komatsu Eeji (e-ji). See Manga Updates for an example of this. While I can see why you might want to Romanize it as "eiji", it appears that most people are not, and there is something to be said for 「えーじ」 being Romanized as "eeji". The publisher used "E-ji" on the cover of the first manga tankobon for Golden Time. The light novel itself does not offer an "official" Romanization for the name.