No way you're going to get it approved in advance in any way that's enfocable. But a 20 hour layover is a pretty solid argument for picking up the bags (short checking). I'd put your chances fairly high, but even if they don't allow it, BA has no real weight restrictions on your carry on, so just take what you need for the overnight there. No one at BA is going to bat an eye at a full size rollaboard. Also even if you don't want to do that, Ireland is packed full of Aldi and Lidl stores, you can get essentials quite easily for very little cost. (Not clothes but pretty much anything else). If you're thinking larger liquids, LHR duty free is competitively priced as well and Ireland is EU, UK is not, so you can take your duty free there.

Another thought, if you absolutely need your bags there, you can change your itinerary to take the 2pm departure on QR instead, that forces it into a stopover, but likely triggers the $125 change fee.