You don't seem to even know what cultivar you're growing. Until you determine what a plant is precisely, you won't be able to accurately determine its needs. I already suggested that you try to grow the strawberry with natural temperate seasonal light variation. If you do that, at some point in the cycle the plants might flower.
Right now you are growing the plants with light that they would only find in midsummer at high latitudes. You could try maintaining that, or you could begin decreasing the light and creating an artificial Autumn, since you are doing this completely opposite to the seasons in the Northern Hemisphere. Do these plants also receive natural might as well as artificial light?