I would agree with your assessment. If the pitman arm is not moving while you're turning the wheel that far, then the play is between the wheel and the box. Not after it.
But... Since the test described is one of my favorite things to tell people to do, I say do that anyway! Hah! Just so you can say you did it.
Heck, you might actually find other things that you would not have noticed otherwise, given that extreme amount of play at the wheel.
Is this a legit five inches too? Using a piece of tape or other marking with a pointer to verify exactly how much rotation you're going through.
What about the rest of the shaft? Is it still an original one piece? Sounds like it is, since you said you replaced the bell/tulip joint.
In spite of them both being new, it sure sounds like there is excessive play in either the bell/coupler, the box, or both.
A quick test should let you know.
Speaking of testing though, it sounds like you've already grabbed the steering shaft and turned it by hand? If so, then you can certainly tell if it's play in the coupler, or play in the box.
I'm sure rebuilt boxes are subject to lots of wear items being re-used. Maybe not always, but if new parts are hard to find, and the old ones just can't be tweaked to be like new, then even a "rebuilt" box is going to have issues.
Hmm, I just remembered that I have a brand new sector shaft still in the Ford box that I bought back in about '82 or '83 from the dealer. I had bought a new box from them a couple of years before, and thought I'd rebuild my original instead.
Funny, but the brand new box from Ford was $175 bucks, while the sector shaft alone a couple of years later was $250 all by itself!
I wonder if I still have that stuff in the garage?
Paul