I have some ideas for a Hawkman movie. These are all just random and jumbled ideas but I will try to clear them up in a single post.
I would make Hawkman and Hawkwoman like the Doctor Whos of DC comics movie. I would make their reincarnation part of their alien culture. The Thanagarians developed the power to keep themselves alive through reincarnation. I would make Hawkman and Hawkwoman aliens, not humans, but when the movie starts they don't know they are aliens. I would make it that the atmosphere on Earth, or maybe being away from Nth Metal technology or Thanagar for so long has made the forget their past lives and who they really are. I would also make Hath-Set Thanagarian too. He is a traitor who kills them, life after life, and because he is Thanagarian he is reborn too.
The movie would 1st start with a flashback all the way to Ancient Egypt when Katar Hal and Sha Ara (spelling?) Hal 1st arrived on Earth. By the end of the Flashback they are hailed as gods and are ruling, but Hath-Set kills them both out of jealousy and anger. Then we go all the way forward to present day Earth where Carter Hall is an archaeologist. Him and Shaira Saunders don't know each other, they think, but something draws them together and opens up Carter's mind to his past lives. By the end of the 2nd act maybe he is Hawkman and she is Hawkwoman. But he is still trying to convince her of their past lives and their alien roots. They are being chased by Hath Set who plans to kill them again. Maybe in a cool visual effect Carter, or Shaira, touches some Nth Metal Thanagarian tech and we see a quick flash of several lives they have lived. As Egyptian rulers, as cowboys in the old west, as WWII era vigilante heroes, as alien cops, etc. By the end of the movie Hath Set appears dead, killed by the two. And while Hawkgirl, Shaira, still doesn't remember she trusts Carter and agrees to partner with him to figure this all out. But it is revealed that Hath Set transfers his soul into the bodies of his many decendants, so like Carter and Shiara, he can come back as anyone at any time.
The movie, like Doctor Who, would have a set up where if the actor or actress wanted to leave they could just replace them with another actor and claim that Hawkman or Hawkwoman was reborn again. And like Doctor Who he/she would look different but could have all the memories and act somewhat similar to the past incarnations.
This might mean that instead of being reborn into a baby like they usually do maybe he/she is reborn as a fully grown adult, just some place else. So, for example, Hawkman is killed in Egypt fighting Hath Set, he dies and suddenly wakes up in Kansas maybe. He is a fully grown man (like Doctor Who the age can change slightly).
Carter's character: Carter Hall is a refined man, an archaeologist who has a grim side. A sadness he can't fully explain. He also has a temper, but only when the person deserves it and never against an innocent person. He seems like he is trying to restrain himself a lot. When he fully becomes Hawkman he seems like a barbarian warrior and a civilized scientist at the same time. He is always ready to explode with rage at his enemies. Because of all his past lives Carter, once he remembers, sees why he is sad. He is constantly saying goodbye to all his loved ones. Countless mothers and fathers, friends, siblings, girlfriends and wifes, sons and daughters. He lives on but they do not, they only get a taste of life.
Hawkman the character and the movie as a whole would be all about life, the shortness of it, taking it for granted, slowing down appreciating life, etc.
But it would also be about love, a love story. Like Raimi's Spider-Man, it would be all about the two and their relationship. Katar and Shai Ara/Carter and Shaira (spelling?). They always end up together, fall in love, sometimes get married and even have children, but they always end up together (and then Hath Set finds them and kills them) but they always find each other consciously or subconsciously.
I'll add more or pretty this up later on.