Very interesting thoughts on the 'one eyed city', littlestan. Like I always say, you learn something new on Wiki everyday.
Still think I've seen an alternative explanation in the 'Lern Yerself Scouse' books, but that doesn't necessarily mean that those books are right. If your theory is correct, it must have more to do with the poor treatment of the Irish in Victorian Cheshire. I wonder if the Cheshire authorities turned a blind eye to the sufferings of the Irish?