OK, just texted a IRL friend of mine whose kids has food allergies and she wrote back:
Use any ONE of the following recipes to substitute for eggs in baked foods.
For each egg, use (ONE of these options):
1 tsp. baking powder, 1 Tbl. liquid, 1 Tbl. vinegar•
1 tsp. yeast dissolved in 1/4 cup warm water•
1 Tbl. apricot puree•
1 1/2 Tbl. water, 1 1/2 Tbl. oil, 1 tsp. baking powder•
1 packet plain gelatin, 2 Tbl. warm water. Do not mix until ready to use
2 Tbl. arrowroot powder
BUT, to be honest, I'm wondering if the egg is even really necessary? I know it's supposed to be a binder but there is already a lot of veg puree in there so maybe just add in a little bit of breadcrumbs, if anything, and call it a day?