So far (keeping my fingers crossed as I write this), since I updated my "messed up phone number" using the payment section inside the "App Store" on my phone itself, everything has been fine on my updates, and I've done several update passes. I had been having that exact same intermittent "Unable to update" problem for _months_. I would try to update and it would give me the "Unable to update" error, I'd wait a while and try again, and everything would update fine. But then a few days later I'd have the same problem. It wasn't until I posted my response above that the "wait and try again" didn't work - no matter what I tried then, I couldn't get past it.
Venturing a probably completely wrong guess, but it _feels_ like Apple has several replicas of the database with our payment information (or several data centers), and one copy had bad payment information. In my case, if I was unlucky enough to be connected to that data center or database, my phone/my apps wouldn't update. When I waited and reconnected, if I happened to now connect to a "good" database, I could update. When I updated my phone number (my payment information) via the iPhone App Store app, that seems to have forced a database update to all the database instances and corrected all the data. (I never actually filed a support ticket, so I don't think Apple did anything to fix my problem, unless someone just happened to see my response above, forward it to the right person, find the problem, fix it, but then not notify me.)
Of course, I might have just had a few days of good luck, and I might now have just tempted the gremlins of Apple Fate by posting this, and I've now caused them to decide go wreak all sorts of havoc again with my updates...