Vegan crepes that don't fall apart when turning

When I make crepes I use eggs, flour and milk for the dough and tiny amount of oil for the pan. I usually use whole wheat flower. Sometimes half-white half-whole wheat. They always end up very thin and perfect.

Replacing milk with various liquids (soy milk, almond milk…) seems to work fine.

I would like to stop using eggs, so I made several attempts with various egg substitutes, and I can’t make it work for crepes. They always fall apart when I try to flip them.

Which ingredient would help with with that?

So far I have tried:

• The Neat Egg
• Ener G Egg Replacer
• flax
• extra oil
• applesauce
• bananas

Those all work for thick pancakes, but (at least not for me) for crepes.

There are questions related to replacing eggs, but are too generic:

• How to make pancakes/crepes without eggs nor any liquids besides water? — not limited to vegan
• What can I substitute for eggs in a pancake recipe? — pancakes, not crepes
• With what can I replace eggs? — a few answers mention pancakes, but not one mention of crepes