Welcome to the group!
You can cut two pieces of pipe that will slip over the bale spears, weld a nut over some holes drilled in the pipe to accept a bolt to act as a set-screw to hold the pipe in place. Then weld a couple pieces of square tube across the pieces of pipe to form a cross frame and weld your receiver tube to the cross pieces. That would allow you to move the trailer easily, then loosen the set screws, slide the adapter off and put it away for the next time. How heavy a trailer are we talking about?
Whatever you do, you need a solid implement like a bucket, forks, or a bale spear to use as a base for your adapter. Others have tried to use just the quick attach frame with no implement on it and bent it quite easily. It has very little torsional strength on it's own, it needs an implement to stiffen it.
As for the bucket hooks, reinforce the bucket lip with something, whether is angle iron, flat bar, pipe, something. The 844 loader has enough power to bend it if you don't. Like gwdixon, I added 4 hooks to my bucket, one on each end of the upper lip, one in the center, and one on the bucket heel. I should have put the end-of-bucket hooks in line with the loader arms, but it's done now. As long as I'm careful to load both chains evenly it's not a problem. We use the one on the heel more than you might think, often for pulling fence posts with the bucket full of material and tools you don't want to dump every time you pull a post.
What kind of critters do you have fenced in? That's quite the fence behind the tractor.
Sean