The Flaming river box starts with a brand new worm gear, so, there isn't really any play in the steering box.
As far as a rebuilt box, it depends on the box. Typically a rebuilt steering box doesn't get a new worm gear, it gets new bearings and seals. Which means if the worm gear is worn out on center, that play stays there. The only way to get rid of that is to install a new worm gear, and the availability of new worm gears for the Mopar manual boxes has been a little spotty. Looks like Firm Feel is offering fast ratio boxes again, which probably means they have some kind of supply of new worm gears. Call FFI and see what they say, they've always been very helpful when I called and talked to them.
I have a Flaming River 16:1 manual box in my Duster. Works great, although I'll say that with 275/35/18's up front and a few degrees of positive camber it's not the easiest thing to steer once you drop below 5mph. "Armstrong" steering, as they used to say. ;)