No doubt if you trace long enough, all of our ancestors were immigrants. I have yet to see any credible sources that show most of Rohingya migrated under British administration. The studies you cited also acknowledged the fact that there were already Muslim communities before the British came. What we are seeing now is a mix-breeding of 1. Muslims whose ancestors have settled in Mayu region, 2. immigrants from the then British India, and 3. local Rakhines. Their identities were defined based on the religions they follow.
Regarding the claim on birth rates, it is universally true that poverty is highly related to birth rates. The Harvard study you cited has already suggested the solution to it: free movement and job opportunities.
I quoted recent GDP figures because there are arguments that they are Bangladeshi citizens. Then, it would not make any sense for them to stay in a country that doesn’t welcome them. The reason must be that they were born in the country.
The ARSA are a group of violent thugs who have no consideration for the suffering of their own people. But it should be noted that they are not well-armed or supported as opposed to the propaganda of the Burmese army. Or there is no evidence they are backed by Jihadist groups yet. You are overlooking the decades-long suppression, restriction on movements, several violent campaigns of the Burmese military that involves tortures and sexual abuses towards women before the emergence of this radical group who are deluded by the idea that if they are an armed group, they can sit at a table of peace negotiations like other ethnic armed groups.
Also please read from sources other than those written by Jacques Leider, a Rakhine historian who thinks just because he studies Rakhine he has to be on the side of Rakhine and Aye Chan, a complete racist.