Hmmm, sounds like you've got some good bits on that SV (color me jealous!
). If physically sliding back on the bike improves the handling for you, then I'd suggest you experiment with reducing the preload on the rear shock and/or increasing preload on the forks, which would effectively shift some of the weight bias towards the rear of the bike (and allowing you to sit normally). There is sag to consider too, so I wouldn't go too crazy with your adjustments (at least not at first).
I must confess though, I am NOT any sort of expert (or even close) on suspension setup. I'm just basing my comments on my own experience, my (limited ha!) understanding of basic motorcycle physics, and various things I've read.
In any case, it doesn't cost anything to experiment. Just be sure to write down your current settings so you have a baseline to measure from (or return to if you totally screw things up