This is more a suggestion than an actual recipe. You need to add things to replace the role of egg. So, increasing the fat content (oil, schmaltz, whatever) would help make up for the missing egg yolk. Adding some gluten to the dry portion of the mix would help make up for the missing binding qualities of the egg white, and you'd probably need to tweak the amount of liquid (water, stock, whatever) as eggs contain lots of water.
I'd be curious to see that too...it is, after all, the egg that holds the whole thing together. I've made them on occasion with just the egg whites (and taking a flavor hit as a result).
Can try adding some potato and/or tapioca starch to the matzo meal to act as a binder, substituting for the eggs.
Just curious...why totally egg free? It is a serious an allergy thing or a vegan thing? If the former, is it all eggs, and if the latter, what do you replace the schmalz (and it's incumbent deliciousness) with (perhaps a kind of ghee made with palm oil and LOTS of onions would be suitable)?