I've already got your trailer drawn out, so I've added the tongue box collision so you can see what to do about replacing it.
I hope this is reasonably clear - it's looking down on your trailer from above and to make it easier to draw, I've swivelled the truck round the trailer (designers with CAD packages have that God-like power!):
Your current tongue box (about 44" wide by 21" long, right?) is shown in pale blue as it the (dotted) truck when it made contact. That's an angle of about 53 degrees from the straight ahead, which is quite a big angle.
The purple lines show that if you made the tongue box 9" narrower (each side), either just narrower all over or by sloping the sides in, you can get up to a 70 degree angle.
But, the thing is that it's only about 6" of movement backwards of the truck to get from 53 degrees to 70 degrees - so this wouldn't make it a "I don't need to watch the trailer at all" type of deal - it would just be a little bit better than it is now.
Sadly, your plan to make the tongue box shorter won't work - you'd have to shorten it to maybe only 6" long before you could keep it the same width.
I don't suppose this has given you an answer that you like, but I hope it lets you see what you can do.
Andrew