A really incomplete picture from what I have read. The Rohingyas did migrate but during British period mostly. They migrated in such a high amount that they soon dwarfed the native population. To add salt to the injury, they demanded separation from Myanmar. And your quoting recent GDP per capita figures is certainly very misleading for migration done in last century.
Did Myanmar have a real problem due to the unwarranted migration? Yes. Did they adopt a right approach? Hell, no!
They could have studied other places where colonialism led to demographic change and settled for a reasonable and humane solution, which ethnic cleansing isn’t.
Of course, as long as attempts at power grab by Islamist is tolerated by Rohingyas themselves, there will be no solution.
Also the Buddhist nationalists are right on the higher birth rate claim. You yourself admit that Rohingyas have been excluded from census so it’s not possible to observe the data about Muslim population.