i slow cook a lot of low carb meals. you are right that you have to be careful of the root veg, so i won't use them and will usually have a smaller portion than i would have had when including root veg (so probably the same amount of meat, just not bulked out because you don't need it really), but i love mushrooms so i will add lots of roughly chopped mushrooms which does add some bulk
you also need to be careful of the quantity of onions as these can be very carby (substitute shallots or leeks)
it does end up being a bit thinner than a normal stew too because you won't be adding flour, but you can reduce on the hob if it's really liquidy
my low carb beef bourguignon (sort of) is:
about 500g shin beef (very cheap and delicious slow cooked)
butter
2-3 finely chopped shallots
2 crushed garlic cloves
maybe some finely chopped celery
glass red wine
beef stock (to taste really, you can top up with water if needed and reduce later if needed)
dash worcestershire sauce (optional)
(also optional is dried porcini mushrooms, soaked in boiled water from the kettle, add both mushrooms and liquid to the stew)
bouquet garni
bay leaf
shitloads of chopped raw mushrooms
brown beef in butter, remove with slotted spoon, set aside
soften shallots and garlic (and celery)
add wine and reduce until alcohol evaporated
return beef and the rest of the ingredients, season as needed
slow cook on low for hours and hours (maybe 6-8?)
if too liquidy, reduce on the hob before serving
it's lovely with kale wilted in butter