I wouldn't do anything to change his appearance or basic history (like being the last of his race) But I would like to update the concept of Martain Manhunter and his story, so his solo book would work on this premise:
Martain Manhunter - (would kind of be like the "X-Files" featuring Martian Manhunter in his secret identity of John Jones (F.B.I. Agent instead of Detective) who has been searching the Earth and protecting it from plans of "world domination" by the White Martians for thousands of years. He would have seen man's worst defeats and greatest triumphs, as he has lived through out the centuries, but nonetheless would defend Earth's right to a natural evolution)
This would essentially make J'onn an actual "Martian" manhunter and give us "UFO" conspiracy buffs a comic book to read. You can call it the "White Martian Conspiracy!"