If the deliverables are provided to a location outside the EU, and the invoicing is done in a location outside the EU, by a legal entity based outside the EU, then it may be possible.
(Somewhat analogous to Amazon taking orders on a .co.uk site from a UK resident, for items which are then delivered to a UK location from a UK warehouse, and then claiming that because the invoice processing happens in Luxembourg, the work itself happened in Luxembourg).
You could then receive unearned income (share dividends, etc) from the company that invoiced the client.
You will need to clear this with legal or accountancy professionals with specific experience of the Irish jurisdiction.
There have been recent changes to EU regulations for remote work delivered electronically without substantial human involvement to non-business end-customers within the EU - the VATMOSS regulations - but you are the opposite case. Your clients are businesses, and they are outwith the EU.