My heart truly goes out to you. What a challenge you've been dealt.
On SLD: It sounds like you're already experiencing SLD naturally. Granted, it's probably stress induced. But I don't think taking oil or SW is going to do much in terms of changing your set point, which is the goal of the techniques. However, it's my guess that you're not getting enough calories and nutrition to effectively burn fat and healthily loose weight. Chances are that your metabolism is extremely slow to compensate for your lack of eating.
For this reason, I'd say give it a shot. But I would not suggest trying to eat less. The SW and/or oil will help increase your calories and perhaps jumpstart weight loss from another angle. Not really sure. It could backfire and totally kill what little appetite you have.
Honestly, I think your weight loss issues are going to be best addressed with exercise and an increase in calories. Just walking 30 minutes a day could drastically change your body's compostion if it's a new activity. Not everyone agrees with me here, but I strongly believe that we need to eat 4-5 times a day. Not necessarily huge meals, but at least SOME nutrition to keep the body's systems stimulated. Maybe you could use oil and SW to help you get to that point, feeding your body something more frequently. If you can, I'd also suggest trying some sort of protein supplements throughout the day. Shakes always work well.