I'm thinking they're not going to be latkes no matter what they are. Here's where I just can't get into the whole Paleo, or LC, or vegetarian or whatever substitutes for the "real deal" (and I'm using "real" here to indicate "authentic"). At some point you have to decide if having Chanukah latkes is that important to you. If they are then make the exception and have a few. If they're not, it's probably better to just have more of whatever it is you can eat and not trying to make almost-always disappointing substitutes.

That said, perhaps some veggie gums may help serve as a binder of sorts. Worth a try.

Guar gum or hearts of palm?

I would cook some yams or winter squash and mash them with the traditional onions and seasonings, form into cakes and fry in plenty of animal fat of your choice...not quite the same, but I can't imagine they wouldn't turn out well...if the mixture seemed too wet, you could add a little coconut flour if you tolerate that.

It seems most vegan latke recipes don't even use eggs.. so I guess you could try just eliminating the eggs.

I recall seeing somewhere an egg substitute with flax seeds, where you put a tablespoon? in a glass of water, stir and let sit...apparently it becomes 'gummy' (try googling egg substitutes with flax seeds)

Don't know if this will work but you could give it a 'test' try beforehand to see if its even worth the effort.

I've used ground flax soaked in hot water. It takes on that "eggy" texture and should do the trick.

I admit my first thought was "Hamburger" but....

A dairy free, egg-free, nightshade-free "latke" isn't actually as paradoxical as it first seems.

Potato rosti have all the oniony, crunchy taste and texture of latkes without using egg for binding. Why not simply replace the potatoes with whatever root vegetable or starchy squash you have to hand? Celeriac would work well, as would a parsnip, carrot and spring onion rosti.

Here's a classic rosti recipe that to provide you with the basic proportions:

http://www.bbcgoodfood.com/recipes/4794/parsnip-and-potato-rosti

Celeriac is another awesome potato substitute!

Sweet potatoes plus a bit of Mochiko rice starch plus yogurt?

Here is a sweet potato and parsnip latke recipe which uses potato starch and yogurt as a binder. I would substitute Mochiko for the potato starch to make it nightshade-free. http://glutenfreegirl.com/sweet-potato-latkes-gluten-free/

GLUTEN-FREE SWEET POTATO-PARSNIP LATKES

Once you have grated the sweet potatoes and parsnips and squeezed and grated some nutmeg, pull out some yogurt. Guess what! You don’t have to use eggs to make these latkes. And if you can’t eat cow’s milk, try the yogurt you can eat here. (I think a coconut milk yogurt might be particularly good. You only need 3 tablespoons, after all.) You just need a binder, a little protein, to hold together the latkes. Frankly, we found out that yogurt works because we ran out of eggs before making the latkes for photographs yesterday.

It’s a new year. Why not eat something for breakfast that is healthy, easy to make, gluten-free, egg-free, and potentially dairy-free?

If that sounds like a mouthful, all you need to know is this: these latkes are a gracious surprise in the morning.

1 large sweet potato, peeled 1 or 2 large parsnips, peeled 2 large shallots, peeled 1/8 teaspoon fresh-grated nutmeg 1/2 teaspoon fresh thyme (the McCormick dried thyme works well) 3 heaping tablespoons yogurt (use full-fat and the kind you like) 60 grams (about 1/3 cup) potato starch kosher salt and fresh-cracked black pepper 1/4 cup grapeseed oil

Grating the sweet potato and parsnips. Grate the sweet potato and parsnips into a large bowl of cold water. Let them sit for a few moments to release their starches. Unlike potatoes, sweet potatoes are not particularly starchy, so you won’t have much starch remaining at the bottom of the bowl in the end. However, you want to remove whatever starch you can. Squeezing out the water. Grab a kitchen towel, or paper towels, and put it over a colander. Scoop the shredded sweet potatoes and parsnips into the towel with a slotted spoon. After you have moved them all over, grab the kitchen towel, close it up at the top, and squeeze all the water from the vegetables over the kitchen sink. Keep squeezing until the sweet potato and parsnip shreds are dry. Transfer them to a large bowl.

Finishing the latke batter. Grate the shallots into the sweet potato bowl. Add the nutmeg, thyme, and yogurt and mix it all up with your hands. Pour in the potato starch and toss everything together. You want the mixture to cohere without being starchy or clumpy. Season it with salt and pepper.

Making a taster. Set a large cast-iron skillet (or similar heavy-bottomed pan) over medium-high heat. Pour the grapeseed oil into the hot pan. (Move the kids out of the kitchen.) Grab 1 tablespoon of the latke batter and put it in the hot oil, gently. Cook until both sides are browned, about 3 minutes. Turn off the heat. Allow the tiny latke to cool, then taste it. Did it fall apart in the pan? Add more starch. Does it need more seasoning? Add that.

Cooking the latkes. When you have the latkes the way you want them, turn the burner onto medium-high heat again. When the oil is hot, add 1/4 cup of the latke batter at a time, pressing down on the top when it is in the pan. Do not crowd the pan. We put in 3 latkes at a time. Allow the bottoms to brown, about 3 minutes, and carefully turn the latkes over, cooking for about 3 minutes. Be careful to avoid oil splatters. Remove the latkes from the pan when they are as browned as you wish.

Continue cooking the rest of the latkes. Sit down to eat.

Makes 8 latkes.