My knowledge of particular diets is limited.
The greek diet thread has some useful articles, and this is a useful article in that in sets out some basic rules, and gives reasons for them.
http://www.ajcn.org/cgi/content/full/81/2/341
Omega six will be stored in fat cells, in cell membranes, in the brain etc so it is going to take a while to "rebalance" the fats in the body.
A trial showed optimum uptake at about two grams of DHA a day which is four to five TPS of a quality fish oil.
Flaxseed or oil your preference (see posts) will provide some ALA and omega six.
I have not seen any trials on an optimal regieme to try and rebalance the body fats. Trials looking at particular organs in animals shows intital uptake is quite quick but can expect months fo some organs like the brain.
Exercise will help burn off fats. Sugar and particularly fructose sugars are linked to weight increase, and can block the pathways that make long chain fats trials suggest.
Grains are possibly best limited as they are not the most nutrient dense food. Variety is good. Green things highly coloured fruit and veg, some pulses, fish, lean grass fed meat in small quantities, fish including oily, the usual things that are often cited.
Juicing adding back some of the pulp or liquidising it for additional fibre is frequently suggested for detox.
Obviously bringing the threes and sixes into balance possibly with more three than six, but watching for signs of long chain omega six AA (archnidonic acid) deficiency - dry skin etc. If your fat making pathways are not functioning that will likely apply to omega six also, but you body may have stores of AA. I suppose testing would be the only sure way to determine your fat status. Some GLA may be useful as that skips half of the fat making process for omega sixes. AA is also found in eggs offal etc.
Please do talk to your advisors about dietary change. They may suggest some blood tests to monitor fats etc. Omega threes do thin the blood which is an issue for some.
I am sorry I cannot give you any more thoughts. The above is based on what I have read, but I have never seen anything on a specific omega six detox.
RB