Well it's too late to change things but for the future I'd like to know about oaking your kit wine.
According to the generic directions for Sgagnols kits, if they give you oak, dump it in at the beginning. No discussion of them after that point. At two weeks or so after reaching FG you then put in all the stabilizers, clarifiers, etc. and rack to 6 gallon carboy and top up. So the Oak is gone after two weeks. Seems like a short time to me, I did taste a wee bit and did not detect any oak.
btw - beer brewing is far more interesting than kit wine. Flames, heat, boilovers - you can't beat it. LOL