I'm with Paul.
In fact, I'd stick a few sheet pans or roasting pans in the fridge or freezer now to chill. Then, when you pull, put the pork, shallowly, in the first pan, stick it in the fridge, then repeat with the other pans and the rest of the pork. The point is to cool fairly quickly. Do the best you can then put into Zip-locs--fairly thinly--and place the bags in the fridge, not stacked on one another, on whatever you've got so that there is good air circulation. Reheat for service.
(Alternatively, pull, pack not-too-thickly into Zip-locs, press out the air, seal, then plunge into ice water to cool. Fridge when cold.)
The thing to avoid is pulling and packing thickly into bags and sticking them in the fridge. The center won't cool sufficiently. Instead, the a scenario will be set up that's perfect for bacterial development, just as if you'd left the butts in the cooler too long but, often, worse, as pulling cause the temps to drop into the worst part of the danger zone more quickly, and packing the bags thickly maintains this for quite some time.