Uniqlo now has larger quilted sling bags. These are quite a lot bigger than the original ones, but are not oversized in a way that would look silly.
Here they are next to the original size
[picture by Uniqlo]
I have been looking at the Baggu medium sling bag, which is a bit bigger than the original Uniqlo one (though way more expensive) but this one might be a great option. For me the biggest advantage of the Uniqlo one has been the price. It costs the equivalent of $18 in Sweden, and at that price you cannot go wrong. My black one has been in constant use in challenging circumstances and it has been perfect.
Tomorrow I will be featuring another sling bag, by Hershel.