I don't know if I am the right person to answer this, because I really didn't do well on Atkins – I lost weight during induction but all that rich food and too little produce had me nauseated and -ehm- constipated

Not to mention that like you said, the occasional cheat would mess everything up.
Here what works best for me: I do not count carbs, but I focus on low-GI fruits and veggies and I limit myself to two fruit a day tops - no more. I never ever limit my veggies, though! I always feel better when I eat lots of veg, and if they are low-GI, high-fiber veggies they never ever mess up my blood sugar.
I don't count calories either because it makes me obsessive, but I do limit my portions and try to choose mostly lean protein and good fats.
Again, this is nothing like Atkins, because you still limit your fats (somewhat, not obsessively so) and are more choosy in picking them, but it still leave you a lot of freedom and a lot of foods to choose from, and it is more sustainable on the long run. And the occasional cupcake or glass of wine won't set you back ages (as long as you get back on track and "occasional" doesn't become "several times a week"

)
I hope it helps a little!