Car crash with Echo's mom (spoilers)

Hey all - loved Rant, just hung up on a couple points that maybe other folks could help with.

On page 255, it is explained Green was hit by Echo’s mom. On page 175, it is explained Charles was hit by Echo’s Mom. This is the clearest link that Charles and Green are the exact same person (the fellow’s name was Charles, but he changed it to Green post-time travel, as explained in numerous other posts).

It is because of this crash that Green/Charles ends up at the year where his great grandma Hattie is 13. They have sex, and afterwords Green feels stronger, and thus he discovers stoking (256-257). Green is 23 when this happens.

Green spends the next several decades stoking himself, and Chester is eventually born. Chester basically lives the life of Rant, as described throughout the book. When Chester moves to the city, he meets Echo, whose arm, as described in the story, is crippled from her accident with Green/Charles.

But this is where I get hung-up: How could Echo’s arm be crippled? In this redo of history, the timeline in which Green is stoking and Chester is eventually born, Green isn’t around when Echo turns 8 to run into her and screw up her arm. Does that make sense? The Echo/Charles accident screws up Echo’s arm, but then Charles/Green goes back in time (way before the accident) and starts messing with history, so there is no reason to believe that Echo would end up in an accident with Charles/Green and cripple her arm in this redo of history.

How is it that the Echo that Chester/Rant knows has a bad arm???

Any thoughts? Am I totally misunderstanding how timetravel is projected to work in this novel?