n/a box will die if you run the turbo motor. best option is to source an lsd either from japan (second-hand) or possible via NZ - i may be able to help you out.
new lsd will set you back about $1200-1800
how are you sure you have a factory lsd with your n/a box by the way? i had a look at an aussie gt rrecently which the owner was certain had an lsd - but it did not.