Thanks for your help. Because of this 34000 miles error, I have to use the AI version. Both new version and AA allow me to fly LAX -> xMIA -> LIM and LIM -> xMIA -> IAH. I guess because I do not have stopover, it does not count as 2 trans-con?

I quickly use EF to search RT fare difference between QR and RJ. It actually differs a lot. That's might be reason why online tool does not allow to have QR as first leg. We will see once we get back from AA