Hi Bud,
I don't think the fact that your savings are not held with an Irish bank has much relevance, as long as you succeed in proving that the money is yours, and that you are not money laundering.
In France, we shop around for a mortgage, and where your deposit is held is quite irrelevant to the banks. In the UK I have the feeling it's the same: if you have a monthly direct debit set up from your current account to a savings account, the bankers can tell that you are not spending that money.
Unfortunately I can't advise you re safe savings/deposit accounts in Ireland. With the exchange rates going up and down, it's really difficult to invest funds in a different currency too.
One advice: once you have saved up enough to start viewing properties, if some of your deposit is held in foreign bank accounts, rapatriate it to Ireland before starting to make offers. I worked in a real estate agency, and although it was upmarket and we had clients from abroad, we really did not like it if they told us the monies for the purchase were currently in Switzerland or whatever. We were burnt once: the buyer, a friend of a politician from an African country, was money laundering... Don't walk into an agency with a suitcase full of banknotes either!
I'm really impressed that you manage to save 40% of your pay: well done!