Interesting story so far. I don't see this Harry as being into cross-dimensional incest, but James wouldn't know that.
So this is the start of the sixth year for Hermione and Ron, while Ginny and Luna are in their fifth year. That would make him about the same age as Tonks. Based off his memories he has a strong idea of where the other Horcruxes are located and what major events may take place this coming year.
The continuing affair with Narcissa is interesting in that it provides an ongoing challenge to Draco for the honor of the Malfoy's and that it might be useful in gaining more information about various DE's.
I'm looking forward to seeing how this story develops and how Harry is going to deal with all of the people in this world that he knew in the other world and with the Potters.
Author's response
Yes indeed, this story basically replaces HBP. Harry, or Odysseus in this case, is five years older so within a year or two of Tonks, who is already pining for Remus as in Canon. Do you think he ought to dump Narcissa for her? Might make for a couple of interesting triangles: Harry!Tonks!Remus not to mention how Draco could now be angry with Harry for both seducing his mother and then dumping her. Hmm. BJH