"But doesn't the whole ketosis/trying to run your body on stored fat thing change this?"
I don't know - I read Atkins years ago (the very first low carb book I'd encountered) and I don't recall how that all works.
" the carb meals are zero fat?"
Yes. You can do things like hummus and whole grain tortillas or wraps and veggies, cannelli bean spread on whole grain toast, whole grain pasta with some kind of veggie sauce as long as you don't use fats in it. You get the idea.
I love falafel! And I used to make Tempeh gravy over brown rice, that was a staple. It was actually nutritional yeast gravy from Laurel's Kitchen cookbook.
Robin Robertson has 3 vegetarian cookbooks out - I ordered them from the library. One is the low carb and one is a slow cooker cookbook.
It sounds like you are tweaking your plan pretty well - keep up the good work!