Can I substitute out the eggs in the filling to make this recipe vegan?

I was a long-time vegetarian and one of the best replacements for eggs that I found, especially for baking, was soft tofu.
It helped cakes and pastries and sauces cohere. Also had some protein and moisture, so similar though not identical to nutritional make-up of eggs.
If you can't find or don't like tofu, use another vegan egg replacement.
I wouldn't use oil. Though it mimics the egg volume, it is way too fatty and will make an unpleasant pie filling.
Last, to make the dish vegan, you should replace cow milk with nut or grain milk.