Not all of the Irish "came through Ellis Island". My forebears arrived in Philadelphia and spread to other states from there. They were granted citizenship right on the ship before landing. All they had to do was to "declare allegiance" to their new country and they were given papers upon landing.
This did not mean that they didn't have to take dirty jobs -- couldn't get much dirtier than coal mining and slate cutting. Many of the men who were old enough to bear arms went right into the Union Army. But the records show that they worked those jobs and others on the side and bought property as soon as they could. The women took in wash and worked as baby nurses and ran boarding houses.
How about removing the "night soil" from Manhattan, one of the few jobs that the early Irish were able to get. Immigrants who want to assimilate are different from immigrants who think the USA should become like their old country....except for earning money.