The cool thing about std. Tuttle and Deep Tuttle fin boxes is that the side fit and base length (at the root of the fin) are identical.
The Deep Tuttle fin root (and fin box) are all the same dimensions as the std. Tuttle, just 18.00 mm (0.709") deeper.
So, just fit your std. Tuttle fin into the deep Tuttle fin box and use fins screws that are 18-20 mm longer.
Fitting is pretty easy (do a search on this forum for "Fitting Tuttle Fins".
If the fin base stands a little "proud" of the bottom of the board, a few strokes with a file on the high spots (use bar soap as a high spot indicator) and it will seat in perfectly.
If the fin root goes too far into the board, you can use clear packing tape to "shim" the front and rear tapers a bit to bring the fin up flush with the bottom of your board.
Again, the main reason for the development of the Deep Tuttle fin box was that for fins with a span (depth) of more than 60 cm there were some strength issues with the std. Tuttle box.
The Deep Tuttle box provides more support area to prevent shear forces from "prying" the fin box out of the board.
Hope this helps,