Where are you pirrad?...I might have a fin box and even a fin that you could have..I'm sure I saw one amongst my junk not long ago.
BTW..How wide is the Tyronsea board?..It sounds like a good idea to get yourself on the water nice and cheap..

As for how far from the end for the fin box..I reckon between 4" and 10" from the tail..about 6" should be fine.
DJ