ianal, but fwiw here's an interesting tidbit I've picked up from lawyers in the past, when in a similar situation: they don't necessarily think of it as "we will own your IP." Instead it's "we will CLAIM to own your IP." The point being that it's not some absolute uncontestable ownership. You're always free to claim ownership yourself, despite anything stated in writing.
Anyway, I thought it was interesting because my non-lawyer brain thinks in terms of things I own and don't own, end of story. But the legal department thinks in terms of arguing ownership and resolving disputes in front of a judge.