To fix this problem, I planned to remove the original binding, and replace it with looser binding (I assumed that the problem was that the binding was just too tight). However, when I started to take the binding off, I discovered that the problem was actually that the sleeves were gathered underneath the binding, not that the binding was too small.
Once I had dealt with this discovery (by unpicking the offending gathers), discovered that the existing binding was actually a good size, I simply pinned in back in place.
Now, all I had to do was to sew the binding in place. My sewing machine is a bit... temperamental... or old, depending on the mood I'm in, so the stretch stitch is a bit unpredictable, and often doesn't stretch. So I opted to use a narrow short zig zag stitch instead (length 1.5, width 1.5). To sew the binding onto my new and improved and bigger sleeve holes, I had to stretch the binding to match the fabric in the sleeve.
And with that completed, my top is now wearable again.