The Ramayana (of which I know the Ramkhien, the Thai version, the best) is a fantastic story. It goes like this:
Once there was a minor god, whose job it was to wash the feet of all the gods going to events in Mount Meru. This was not a good job. All of the lesser gods would kick him, mock him, etc, and treat him very badly. He went to complain to Shiva, who granted him a boon (a favor that cannot be denied). This god wanted to be immune to harm from any god. Shiva granted the boon, but Vishnu was angry with him because this could spell trouble, and so it did. This god was reborn on earth as Ravanna, a ravaging king (in Sri Lanka), who could do whatever he liked - he was too powerful for any mortal, and immune to the gods. So Vishnu himself was reborn as a human, Rama.
Rama had a beautiful wife, Sita, and Ravanna heard about her and kidnapped her, taking her to Lanka with him. Rama gathered together a band of the mightiest heroes in the land to fight Ravanna and, over a long time, defeated the demon after many adventures.
If the plot of "hero's wife is stolen, so he has to assemble a band of warriors to get her back across the sea" sounds a little familiar, it might be. The Ramayana has connections with the Iliad, at least according to some. Or it might be a coincidence. But the story is definitely a religious one. Ayodhya and Lanka are certainly real places, but the myth is deeply intertwined with the stories of gods and heroes.
Putting Rama in the game would raise a few questions:
1) Rama is a living god. Unlike Hercules, Athena, etc., people worship Rama today in India. In Thailand, the kings of the present-day Chakri dynasty are all named Rama (e.g. Rama I, Rama II, Rama III) as their title, as he is the perfect king (IN THEORY), being an incarnation of Vishnu. Putting him in the game would be like putting Jesus in the game.
2) Clearly this would be a mythic hero. That might work if we had an all-mythic leader group - we've already got Maui and Gilgamesh; this would be like including Achilles, Quetzalcoatl, Arthur, Vainamoinen, Coyote, etc. Some of these names would be most appropriate to something like Heroes & Legends, but with a focus on actual historic people, Rama might seem out of place. It might be a slightly different game, too - magic, monsters, demons, dragons, oni, tengu, yakshas, nagas, etc. Cool, and something I'd love to play, but a really different feel from what we have now, vampires and heroes and zombies aside. I love mythology, and H&L, SS, and Z allows you to dabble in myth (urban legend, ancient myth, and pop culture in the above cases), but the feel of such a game would be different.
3) To reiterate #1 - again, this is a god that people worship today. So having Rama opens the door to having the Jade Emperor, Coyote, Jesus, Ogun, et cetera. Which is cool, but seems to be a bit of a hornet's nest (I don't know about the others, but I know there are Christians on this thread - declaring war on Jesus might feel... weird, no?). A safer bet would be to go with gods that do not have worshippers today (Thor, Hercules, etc). But... again, that's a different game.