Howdy! In general that reflux would be excess bile flushing from the liver backing up into your stomach... the usual advice is to drink water to dilute it (sip the water rather than chugging)... and of course you should be keeping your colon very clean, every fsting day, so that this kind of waste can flush quickly from your system.
What colon cleansing rituals are you using? Many times I have had a plain water enema stop a crisis dead in its tracks! If you are behind on your colon cleansing, I would suggest you do one asap.
Meanwhile be sure to keep drinking water, even though you may need to take small sips frequently, as opposed to drinking a full glass. Your body needs to be well hydrated to deal with the fast, and with this reflux issue.
I have large admiration for you folks who are fasting and WORKING! I cannot imagine working on water, though I have maintained a very full routine (including the gym) on juices.