I am a card carrying Kawi guy but the 650 kaw is a massive pile of steaming monkey dung compared to the SV, for the love of all that is holy say away from the 650 kawi.
Seriously get a SV if you want a small twin, Jason Smith has a vintage SV with a blown crank that this winter we are going to replace so he can sell it, already have the crank so a few gaskets and bearings and we are good.
It is a 2mm big bore with FCR flats and he has a good bit of spares and I don't think he ever crashed it, it has good suspension on it so would need to spring it to your weight.