I hate to break it to you, but a Soul Gem IS your mentality...
But no, what I meant is that you overwrite yourself in the new timeline. Homura's contract will always be a decision she made and so it carries with her. In Homura's Revenge, when she grabs Madoka and loops, Madoka wakes up in her bed with all her memories. When Madoka contracts to save Homura, she declines going back with Homura a second time because she'd just be contracted in the new reality.
....which is why I argued against the headcanon of Homura having a shitload of Grief seeds in her pocket from other timelines. That's impossible. A Grief Seed is a soul, and thus it would 'wake up' where it 'should be' in the new timeline. And if the Witch wasn't a witch at the begging of the loop...
Well, Sayaka's parents would wake up to their daughter being dead and then their entire home would become a concert hall as a mermaid knight fills them with swords.