I don't think having ILR makes a difference. Your best option would be to wait and obtain British citizenship and you can move there with no restrictions. If you are married to a British/EU citizen, you could move there based on being their spouse. However, the Irish have been taking well in excess of 6 months to process these applications and are keeping the passports. If you were to manage to get your passport back, they are not giving multiple entry stamps while they application in under consideration, so you would essentially be stuck there until it is processed.
You could also try for a work permit. But, unless you hold EU citizenship, you would have to start over, visa-wise.