Is there any other special reason to say "I don't have time to stop" instead of just "I don't have time"?
No, there isn't a particular reason for using "stop" here. Rachel probably means that she doesn't have time to "stop working," but she could have also said "I don't have time" and the meaning of the sentence would have stayed the same. Ex: A: Would you like to sign our petition sir? B: I'm sorry, I don't have time. Ex: A: Can you grab me a coffee from the cafe? B: I can't, I don't have time to stop by.