Everybody's situation is tough to provide good answers. I've been following the real vitamin trend of healing, cause synthetics seem to not have that ability. Reason being, synthetic vitamins tend to cause more problems than anything else based on first hand experience and reading other's works. Have you read much of the advice from places like: http://farmfoodblog.com/healing-digestive-disorders/
I noticed you originally posted coconut and olive oil, what about other high-vitamin oils?
Here's a snippet from the link: "Use High-Vitamin Fermented Cod Liver Oil (CLO) daily: Provides true vitamin A, vitamin D, EPA, and DHA, among other factors. Only buy high quality brands (only Green Pasture and Premier are worth buying), because most CLOs on the market extract the natural vitamins and add back standardized amounts of synthetic vitamins!"
From many of my prior readings, an investigation into many brands of olive oil, even extra virgin, they found that MOST were mixed with other oils like canola - even though it was not labeled as such. Our labeling laws are garbage when investigations reveal that we've been lied to consistently from many and multiple companies.
Try some non-sweetened or low Sugar
locally grown organic fruits on an empty stomach. Sometimes foods grown in your own region and in season offer more benefits. It goes against the GAPS diet intro, but you could always experiment to see if you can tolerate fruits that grow in your area.
Again, listen to you body's response, cause only you can ultimately determine what is best.