Why might my inner tubes be getting consistently punctured?
So, I think the problem is that I have a 25mm tyre on a rim designed for narrower tyres. That means the rubber surrounding the valve is distorted into the narrow valley of the rim, which puts stress on it. As @Batman suggested, failure #2 seems to be a red herring.

So, I've opted for the narrowest tube available and furthermore used a cutting from an old tube to provide padding around the valve, like this, so that the rubber doesn't have to distort so much to reach the base of the rim valley.

It's still inflated so far, will mark this solved if it's still inflated at the end of the day!