There is no tax issue with transferring your savings to the US - unless there is no question of the funds in your Irish accounts (and any interest earned thereon) ever being "hidden" from the tax authorities in the US, where as a green card holder of long standing your are taxable on all earnings worldwide.
Just open a bank account in the US and deposit your funds, via cheque, international funds transfer or whatever method suits you.
And get a better US tax advisor. If you're in NYC I can recommend someone.