I think if people saw where their balloons end up when they release them with messages for loved ones etc, they'd think twice. It's not as romantic to see it stuck in a bush in the countryside being eaten by (and killing) wildlife.
.... your first move is ban balloons? ...
Like: nothing in between? Maybe a tax or something? Just wild stuff.
Also helium might be scarce soon. Problem might solve itself. (Assuming it's a real problem in the first place.)