Pretty sure that no secondary version Hime is going to get an Awakening, ever. That does include Fire Mammon.
Unfortunately, I don't have good advice for you. Since you already have Fire Frey, and Haruhi will never be an option, my knowledge of Fire just isn't good enough to say.Getting a guaranteed 2 free turns in literally any content isn't weak... but yeah, when compared to Byakko, it's less versatile I'd say. You could always get Byakko and run it in Fire, in most content. IF you have the bricks.