What ingredients can I add to food or gum recipes to add grittiness without any carbs?
Baking soda is commonly used as a mild abrasive in toothpaste, and is a food ingredient. 

Liquorice root is like a tasty chewy twig, and is chewed to clean teeth in some countries. Maybe you could chop some of that up if you can get it. Assuming the flavour is acceptable of course.

Otherwise you might be looking for seed husks of some sort, dried and ground. Cardamom perhaps? It's cooked in pilau rice and while you might choose to eat round it, accidentally biting into/swallowing a whole pod is normal. You'd have to experiment with how much of the flavour you can handle, and indeed with his much is in the husk. 

Have you looked for traditional toothpaste recipes for ideas?