This is going to be an unpopular opinion but try and hear me out.
With a history of eating disorders, the LAST thing you want to do is get back on yet another restrictive diet. And yes, paleo/primal is highly restrictive (no legumes, dairy, grains, high sugar fruits- no matter how whole/natural they are). Plus, you've already been down this primal road before and yes it worked but it didn't stick. Is it because you failed or did the diet fail you? Granted, some people thrive on a low-carb restrictive diet (under 100g), but you may not be one of them. It may be time to be a bit more open minded about this and listen to your body.
Ignore the primal carb curve and focus on eating whole natural un-processed foods that you like - be it potatoes, rice, corn, beans, fruits(all kinds) and veggies. And if you're like 99% of the population and don't have a legitimate gluten allergy, eat whole grains as well. If you don't feel like cooking/prepping, eat fruits for a while or buy frozen veggies to skip the washing/chopping step. If you eat lots of plant foods and less fat, you're going to be full and won't need to obsess over portion size because you get a large volume of food that is also low in calories. The weight will come off without you starving yourself.
The bottom line is that to lose weight, you need to expend more energy than you consume. Whether you're eating high carb or low carb, it doesn't matter. Calories matter and a calorie deficit is required to lose weight. In your current state, I'd say go easy on yourself and stop the fasting/bingeing/guilt cycle. How? Be FLEXIBLE. Allow some cheats into your diet. But don't keep a supply of junk food at home. If you feel like an ice cream, go buy a small amount (not a half-gallon!!) If you want crisps, biscuits etc, buy a small pack and be done with it. No guilt involved. Give yourself a generous 10% or even 20% calorie allowance to eat whatever junk you want. For starters, do this only once a week. If you're mindful of total calories, you'll be surprised at how manageable and effective this way of eating is. If you know that it's not forbidden, there'll be no inclination to binge and eat everything in sight.
I tried the low-carb primal diet for years. All I got was a limited food choice (coz I love starch, dairy, grains, beans and very sweet fruits), low energy and like you, guilt when I fell of the wagon. It's not worth it. Now, almost 80-90% of my calories come from whole natural unprocessed foods. This includes starches and straight up sugar in my tea/coffee. My new diet is 70% carbs and I've lost most of the fat I needed to lose (still working on the last 10). I have a raging sweet tooth and MUST eat ice cream and chocolate on a weekly basis to avoid feeling deprived. But due to my flexibility, I'm actually eating LESS sweets than before (no guilt ridden binges). In 3 months I lost 20 lbs of fat, gained some muscle and I'm looking better than I have in years (currently at 135lbs) all thanks to my flexible (sugar&carbs-are-not-evil) approach.
As for exercise, what works for me is high intensity cardio. I've found that my rate of fat loss is directly proportional to the time spent on high intensity exercise. The higher the intensity the faster the fat loss. And if it works for someone without a lot of fat to lose, it should work wonders for you. At 30 yrs, your max heart rate is 190. Find ANY kind of exercise that you enjoy, that you can do consistently and that keeps you above 75% (over 143) for at least 5-7 hrs per week. Do what works for YOU. Good luck!