Not sure if it's *still* there, but there certainly used to be a Bank of Ireland branch in town... St Vincent Street, I think. Pretty sure there was an Allied Irish Bank as well...
Apparently Allied is for business customers only. Will phone the BofI on Monday to see if they will do business with a non-customer. Would certainly solve my problem. RBS says they have international bank drafts, but unless it would clear in Ireland I am thinking it won't work.
Edit: apparently no BofI outside of Ireland these days.... Yeah, sorry, I'd forgotten that I'd already tried to find Irish banks in the UK with no luck.
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Edit to Edit: Was looking at Ulster bank and it says one can go into a branch, or RBS branch, so apparently they are connected. Will just go into RBS next week and try to talk to someone other than the person at the front desk. (I thought dealing with the UK govmt was fiddly, but the Irish govmt makes that seem easy!)