The tapers and side fit of the Std. Tuttle fin root will fit the deep Tuttle fin box perfectly. It's precisely the same configuration and the bottom of your board, the Deep Tuttle just extends a bit deeper.
You will need 2 longer fin screws to reach the barrel nuts or fin root threads.
You may need to do a little fitting to get the root to fit flush with bottom of the board, but the longer screws
are really the only change.
It will work perfectly!