Check out The Lenders Network they work with a few Mortgage companies here in CA that have approved many of my clients with low scores.
In the meantime, call a credit counseling agency and fix your credit.
Or, just buy cash!
Not really. As long as you have US Credit, it will be considered for any US purchases. With that much cash, you would be well served to resolve your credit issues here, establish some good practices and get back on the American credit bandwagon. It can happen and could happen quicker than trying to establish Irish credit.
Last year I had a British family buy a home. They had to complete 2 years of US residency, provide taxes, income documentation and everything else any US Citizen would. Foreign credit would do nothing to resolve your US situation based on my experience.
I have Canadian Buyers contact me regarding credit and financing issues and even they have limited options.