I have recently started a whole new track on a KISS Veggie low carb diet. I eat :

Eggs
Cheese
All fats
All Nonstartch lc veggies
(infrequently small amounts of chicken/fish)

I'm very happy eating this way.
Digestion good.
Hair good.
Weight good.
Skin good.
Everything good.

I might eat a piece or two of chicken if it's on
a salad at a restaurant for example, but I do
eat alot of eggs and cheese. I never count carbs -
and my appetite seems to limit the carbs
automatically for me...I get full fast.

NO processed foods (cheese is not really processed)
By processed I mean machine/mechanically produced,
in a cardboard box or contains additives and preservatives.
I think you know what I mean without getting nitpicky.

It's possible. Vegan low carb is primarily wonderful veggies, salads, lots of favorite fats (healthy of course, not trans or hydrog) and good protein sources...eggs, cheese (very rarely some fish/chicken) but mostly vegan meals.

It can be done. Dairy products do not stall me, cheese does not constipate or stall me/I'm convinced all the veggies I eat prevent that. Lots of water - and success.