We've had our pigs reach as much as 65 meat quantity. They take longer and longer to butcher, especially with longer break between culls. We've had two people in our village who volunteered to take care of the animals quit from boredom and attrition and both cited butchering as the most tedious task.
My solution: the butcher animation plays once, you get all items instantly, including those from skinning and cleaning. If it fills up your inventory (and any open containers) you get an error message reading something like "You have no space to receive items" and you receive all the items you can hold, and have to repeat the process to get the rest. There's already hotkeys for dropping all of a specific item, so it's still faster if you only want the meat, for example. Also maybe you could do this all with just a right-click, no flower menu required.
I think this should include collecting bones too, but because I know you like it "immersive and cute", you could probably repurpose the hand-harvesting or foraging animation for collecting bones, if you could remove the plants being pulled up from it. This would actually make the process of butchering even longer but it would look better, and with the other changes I think that would be fine.