It is definitely doable. Quite a few people have installed the Nismo LSD. I don't know if anyone has done it as a DIY job (I don't know that you'd want to), but you can definitely get a dealer/shop to install one
Limited Slip Differential. It basically gives you more traction by sending power more evenly to both wheels. Somewhere between positraction (both wheels pull equally, but bad for your car's rear end) and open differential (one wheel spins while the other just sits there and looks at you funny.) I can go more in depth if you want.
I asked my dealer (Brown's Fairfax Nissan) when I first got my Z and the I think they wanted like $1200 for the part and $300-$500 (estimated) for labor. I was like, riiiiiight. Eventually I'll just do it myself. I found the Nismo one for $850 online, though i forget where. I think someone told me it's like a 3 hour job, assuming you have the right tools. Not too bad in my book.
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