I didn't say that EFA's prevent ketosis: it's just that give the amount of polyunsat. fats relative to saturated fats you seem to be at destitute for EFA's (omega-3's=>EPA/DHA more specifically).
And just on a side note, most people cannot enter ketosis unless the fat intake is 55%+ of over all daily nutrient intake, rest being protein, and a nominal (NOMINAL!!!) amount of carbs. All the carbs (if any) on ketogenic diet should come from veggies (along with fiber) and from occasional sweetener/food presevative like those in pepperoni, ham, deli meats (that's why I don't advocate eating that trash)
The issue must be most pertinent to you because you'd want to yield every conceivable benefit from your cycle - accomplish this with an excellent/well expounded dietary routine, no less