JGN, just to mention couple of points. 1. Rama was called Maryada Purushottam - the best among human beings, as known to those at that time, based on his principles of fairness, bravery, etc. 2. Krishna also existed. The excavations in Bet Dwaraka show the submerged Dwaraka City.
In Hinduism, we have the pratice of defining a role model - anyone who has achieved something that is beyond the capability of a large mass of people, is deified (or demonized based on whether it is good or evil act).
If we can call Shirdi Sai Baba or Puttaparti Sai Baba, as an incarnation of God and worship him, why not Rama or Krishna.