To keep your ride near where it is now, sway bars are the best option. You'll find the car skips a little more around the bends, but the improvement in chassis response more than makes up for it.
As a NA 350Z owner, I'm not entirely sure what you're talking about. The Z has more grip than grunt.
It does have axle tramp issues off the line due to the suspension geometry, and that's basically unfixable since its a function of how much camber the rear gets when it squats, but around the corner its got a crapload of grip in the rear. At the limit it does wash the nose if you're not progressive on the throttle, but getting rid of the staggered tyre setup fixes that (you will lose TCS/VDC but ABS still works). The thing doesn't start to oversteer unless you deliberately provoke it, and to keep it sliding once it breaks loose you have to keep clutch kicking.
Fair enough if you're doubling the power and torque by going to a TT kit then you'll find you have traction issues, even with R-Comps, but that's true for any 2WD car. You can't pin that as a "350Z" or FM platform issue.
If you don't take the car on the strip or circuit that often, and you just want a suspension setup for the winding road, I'd recommend doing adjustable swaybars first. If you're still finding it a fraction too soft for your tastes, then get a set of 350Z springs with Koni Yellow adjustable dampers. I've ridden in a few Zs with quite a few aftermarket suspension setups (Cusco, Zeal, Tein, Bilstein, HKS) and my favourite for street use was when I had OEM 350Z springs with Koni Yellows and adjustable swaybars.
Does your car have the LSD? I know that, historically, viscous LSDs have copped a bad rap, but the one in the FM platform cars actually works quite well. If you can't afford to buy a Quaife, and I'd avoid all the clutchpack LSDs for street use, then make sure your car has at least the OEM VLSD.