New Kv = Constant / New Nr.Turns
Constant = Old Kv * Old Turns = 2000 * 17 = 34000
New Kv = Constant / New Nr.Turns = 34000 / 6 = 5666 (New kv)
You're about right on the new Kv but it will be unlikely to be able to turn the old prop vwithout buring up. As the Kv goes up the prop size needs to go down.
And depending on your ESC, it might have some trouble keeping up with the new permutation rate for the much higher Kv.
If you need some smaller wire here is a source: