There are a couple tricks you could use:
1) Try to enjoy your suffering rather than fighting it. You can make light of your moralizing like this, "There I go again... haha. I'm just like a moralization robot."
2) Realize that you can drop your moralizing at any time. The point of the mindfulness is so that you finally realize, "Ohhhhh!!! This is causing me so much damage. It's so pointless. I would be a fool to continue shooting myself in the foot. I will just stop." And you stop.
Awareness Alone Is Curative doesn't mean you need to keep doing stupid stuff for months at a time. The point of it is to SEE your own stupidity and then drop it as soon as you're willing. If you're not willing to drop it yet, then keep up the mindfulness until one day you will become ready.