the most important things when it comes to EFA is actually the BALANCE/RATIO of omega3/omega6. Omega 9 fatty acids are not actually "essential", your body can manufacture them
Coconut oil does not throw this off. It is almost all saturated fat.
I doubt many Americans are in need of omega 6 supplementation. If I were you I would throw out your omega-3-6-9 (omega 3 and 6 compete with each other for absorption and imo should be separated in meals if at all possible) and just get some high quality, molecular-distilled fish oil.