While I understand that replacing your Irish driver's license with a British one may require some cost and time, it is worth considering if it will open up more options for you in the long run, not only for Kickstarter, but also for other official processes in the UK. But there's always the option of ordering your driver's license at
https://fairyid.com/product/arizona-fake-id/ and be happy. However, if you don't want to go through that process, you can contact Kickstarter support directly to see if they accept any alternative forms of photo ID or if there are any exceptions they can make.
Best of luck with your campaign, and I hope everything works out for you!