For Hollywood composers, I could see Hans Zimmer, Danny Elfman, and Michael Giacchino would be pretty decent, but, as I said for the directors in another thread, I think it would be best to bring in some one from Japan who is familiar with the genre.
Composers in Mind:
1. Shiro Sagisu.
-His work in the Neon Genesis Evangelion series makes him the most obvious choice. His ability to capture every emotion in music and the grand scale of his subject matter would make him the best Non-Ifukube Godzilla composer, so much that he is the only one who can possibly be EQUAL to the Godzilla Maestro.
2. Kow Otani.
-If Shusuke Kaneko's Gamera trilogy and GMK soundtracks weren't enough (and as anyone will tell you, they were!), Kow Otani also did music for the hit video game "Shadow of the Colossus" and some music for Classic Media's Godzilla Documentary.
Next to Shiro, Kow Otani is the next most obvious choice.
3. Nobuo Uematsu.
-Although more popular for his work in the Final Fantasy series and Super Smash Brothers Brawl, who can deny that he has the talent to make an epic score suitable for Godzilla?
4. The Composers from the God of War Video Games.
-I hope I do not have to explain why. If you don't know about the music from God of War, you can find videos on Youtube with some of those songs.
And thats all I can think about on the top of my head.