this is bulls**t, Ireland is very much CFC compliant (mostly due to EU), those companies simply have enough substance to be tax resident in Ireland (well, not the US companies but their Irish subsidiaries)
Yep that's about it. The risk for an offshore bank is too great to accept a US client (and accepting US Dollar) as they can easily lose their license over it.
Do a Canadian LP/LLP and open a US bank account due to the fact that your client is US based.
As a US citizen you should find opening a US bank account for the firm very︀ easy, and you have a totally valid reason as to why you want a US︁ bank account given US client. Have an answer ready to explain why you have chosen︂ Canada, and not a US company registration it probably will be asked.
In your particular case I believe there is no US bank that caters to small business that will refuse you (based on what you have shared here, they might refuse you for what you have not shared here though).
For the rest of us the best bets tend to be Canadian banks in the US ... BMO Harris maybe best bet.