The majority of Dunlop Sport Maxx TT's are made in Japan, smooth and quiet with good levels of grip (asymetric design).
The Toyo Proxes 4 is also made in Japan but is an older design not as quiet and smooth (directional design) but will still give decent grip in wet and dry conditions. In terms of flat out performance in the Toyo range it goes R888 > R1R > T1S > Prx 4 > Teo Plus. I ran the Proxes 4s on my Mitsubishi Legnum and they were good, however that had quite a bit more grip then your average R32 GTS-T
If you are indeed chasing "loads of grip" I would still be looking at something like the R1R or Yokohama Advan Neova AD08, in your 16" sizing they shouldn't be out of your budget.