It's just like the Little Red Wagon you had when you were a kid. And those sucked to back up too.
Used to have competition events at the county fairs where kids would see who could back one through a couple obstacles in the best time. (These would be your standard 16' hay wagons.)
When we're in a hurry and have several that need to be backed into the barn, we just unhitch it -- have someone walk along and guide/steer the tongue while a small tractor pushes on the front of the wagon with the FEL. It's easy to steer it in by hand and put it right where you want it. But our wagons are rough wood and we don't mind scuffing them up a little.
A few years ago when you could still find kids that wanted to bale hay, we just pulled the wagons into the barn and unloaded them, and then pulled the hitch pin and pushed it out by hand. Much easier and quicker to steer it out by hand than try to back it out with the tractor.
2nd best option is to have a hitch on your FEL bucket so you're facing the wagon and can see what you're doing.
If you're hitched to the rear of a tractor, best to put it in low range and go very slow and just focus on getting it lined up and straight and then keeping it there. I don't even try to back it up with a truck.
And if the wagon is empty, and on flat ground, it's usually pretty easy for a couple people to roll it around by hand and just steer it by hand.
What are you planning to use it for? It looks to be pretty high off the ground, pretty heavy duty with duals on the rear. What's the plan?