How old is your baby? Is he/she eating anything else besides breastmilk yet?
In my opinion, taking the oil or sugar water is not likely to cause any problems with the milk, but it is really important that your intake stays high enough that your milk supply is not jepardized. I would suggest that you do SLD, but have a structured eating plan to follow to ensure that you get enough of the right nutrients. That way you will benefit from the "reduced cravings" part of SLD, and make healthiest possible choices, but still ensure yourself of an adequate intake.
In other words, plan yourself a really healthy diet of maybe 1800-2000 calories, then add the oil, and see what happens. Hopefully, your "nursing mom" hunger levels will lead you to the right amount of food.
I don't think anyone has tried to hypothesize about the effect of breastfeeding on the setpoint. I just know from personal experience that my weight didn't want to move down while I was nursing. But I also remember that I loved nursing above most other things, and wished my kids had kept at it for longer (they did 9-10 months each, but that was years ago - they're teenagers now). It's a warm, wonderful thing!