...they gave me the sorriest piece of junk they could find it seemed like...
Nah, that's pretty much par for the course with this fleet. You get used to it...some are definitely better than others, and you were probably in a spare.
You'll also get used to backing...if you've never backed anything as large as a package car, it takes some time before you get used to the length of the vehicle and the swing of the back-end. It's really all about the mirrors and the back-up camera.
Depending on where you need to back and how much space you have, you'll get the feel of where to pull the package car into the space available in forward gear before you start your back (all the while fighting the manual steering).
Aside from practice, practice, practice, one hint about maneuvering these trucks is that when you need to make a three (or five) point turn, at the very last bit of motion while the truck is still moving (but you've backed off the gas), you can give yourself about a second to really crank the wheel in the direction it needs to go before you come to a complete stop- so much easier than trying to turn the wheel from a stopped position.
It becomes second nature when you do it dozens of times a day.
Practice, practice, practice!