I am not sure I understand what Acid Reflux is, but I do know that OP is a pretty powerful stomach stimulant for me. Larry and I were discussing this recently around sesame oil -- the way your stomach responds when you are swishing the oil in your mouth! You are signaling to the stomach that fats are on the way, and I am sure its response has something to do with your discomfort...
Can you eat a little yogurt or something before you OP?
Also, I would just try to do the original protocol as much as possible for the first couple of weeks to establish how you react, etc. 1x/day with sunflower or sesame, for 15-20 minutes if you can. Then you know what your baseline response to OP is and your body can adjust, and you can shake things up a little bit!