Welcome to Pakistan in advance, Andrew 
Firstly let me confess that neither myself nor the majority of the travelers on this forum would ever have been to Tuftan! You might already know that the area is far flung, too remote, and seriously underpopulated and many of the problems are basically associated with these factors more than they do with the law and order situation.
I have met quite a few foreign travelers including a solo female traveler, a young French couple, and most recently a Latvian guy who have done this route without reporting any significant issues other than the usual ones, i.e. the hectic journey, bad roads, and the language barrier while crossing the border. Last year a friend of mine drove his car all the way from UK to Karachi and was also worried about this part of the journey but things went smooth.
Now coming to the original question, I doubt that the border is closed. Which British travelers you are referring to?
About the Jiwani border, I guess there is no immigration yet with easy border crossing options with other dangerous and unrecommended means. Note that people living in the bordering districts enjoy relaxed rules while crossing into Iran because of the ethnic relationships (Baloch) and some even have dual nationalities. So border crossing from other places might be doable for them but not for ordinary travelers including Pakistanis.
So Tuftan is the only off-the-beaten path of this route [
] and I would suggest you to stick to that.
Further I would also suggest you not to exclude the idea of traveling in Pakistan, especially around North. There is a lot to be missed I bet. The Latvian friend I mentioned above also wanted to just 'cross-over' but eventually exhausted all his visa period (one month) and wanted to extend that when one family invited him for the marriage ceremony while wandering around Lahore!
See some of his experiences here:
Where are we runnin'? | Facebook
Btw, PakWheels is just the right forum to see what Pakistan has to offer!
Hope the above will be helpful for you in planning a better itinerary. Give me a PM should you need any further information.
Cheers
Muzzammil
Muzzammil's Travels: Round-the-World Honeymooners: Benoit et Marie
