There's a whole bunch of questions that need to be asked re the overall chassis before you decide to go making it AWD. That is, in a word, "dynamics". Having watched a leonie and then a wrx in action I can say, Subaru worked very hard to get the WRX right in terms of chassis dynamics. Part of that was differential setup and power transfere (front rear). I'm no expert on the workings of this, but what you are aiming to do with putting an STi drive train in a buggy provides you with all of the same challenges but without the support of a multinational car company. I'm not saying it can't be done, but there are better ways to spend the same money often.
ask yourself this question before you spend anything (more) or do anything else.
"what specifically am I going to use this car for?"
you can only have measurable outcomes if you can answer this question in a few phrases. You've said so far...
"The buggy will be for road use"
I don't consider this to be specific enough. What road, how fast, motorsport yes/no, if so what class, number of seats/passengers; These all need to be worked out and all effect the outcome and whether it's a success.
My current car has this aim;
"to be competitive in club dirt khanas 12 times a year and stayed registered for basic transport duties." I don't consider it to be a success in the first of these aims.
The other thing worth saying at this point is, dune buggies (and all aircooled VWs/porsches) have some basic handling/suspension design flaws that can sabotage the rest of the car. There are easy solutions to some of these issues, but the solutions make registration more complex. This is because they jetison key bits of what would be considered a "classic style of buggy". I reckon if you want to see what a fast street AWD buggy should work like, look at a porsche carrera4 cabrio and that is a good starting point. Meeting that will involve a similar setup in terms of chassis and weight distribution. Read every article you can find on AWD porsches to see what journos have said about their dramas and what they need to work properly.
Sorry for the essay, but if you figure this out now, it will save you a lot of cash and heartache. See, anyone can fit a 300hp turbo motor to buggy. Whether it's a success as a total car is another dilemma altogether.
P.s. I really think turning the subaru box upside down is the answer to using it in the back of the car, although you need to figure out oil supply well. Start talking to the rally guys for answers to this question I reckon. MRT (Middleton Rally Team) would be a good start.