I've never seen 250-exposure lengths of bulk film sold like that. You just have to wind off about a third of a 100' roll directly into the cartridge using the winder that's available. (Just about all those 250 exposure backs were made by the same 3rd party company, tailored to each specific camera manufacturer, so most of the parts don't actually interchange, but I believe any branded 250-exposure winder is as good as another Nikon/Canon/Minolta/etc.)
I always put generous leaders on mine and still got three full cartridges out of a 100' roll, so right about 33.3 feet is full length with leader. 31.25 is I believe just the length of film that holds the 250 images.
I have the big Nikor tanks and reel that I believe hold a full 100' (no they're not for sale!) They made smaller versions but I've never seen them in real life or on ebay. I guess the 50' one would be easier to use for 250 exposures. When I had a 250 exposure back (original Canon F-1) I was shooting slides and got them professionally processed in a roller transport processor. I've now got the F-1n and the FN-100 back and I can do B&W in a big Jobo tank (forget the numbers) designed just for that. I popped off the cog and use a normal orange rubber lid and just inversion process it. Uses a lot more chems than roller transport, but they're cheap. I also purchased some of the Hewes reels meant for FN-100 film lengths (15-ish feet), plus the loader but have yet to find a tank they'll fit in. The Nikor long-roll 70mm tank is sooooooo close, but no cigar. With the proper winder you could easily load your 250-exposure carts with just 100 exposures if you wanted to use something like that. Buying them from Hewes is an adventure, but I'm sure it could still be done.
(I actually load 108 exposures, so it's an even 3x36, and that fits just fine in the cart with generous leaders. I guess FN-108 wasn't as cool a product name!)
Duncan