Quite an experienced mate of mine went round Spain on his new CBR600F 2 up and full hard luggage with his preload on 1.
Pointed out the error of his ways and wondered how the feck he got round any corners.
Good ol' Honda neutral chassis eh!?
So bung up the preload adjuster a couple of notches and try that. More if needed. If you are doing a proper run out blow a few extra PSI in the rear tyre. I usually will put in 4 or 5 extra PSI.
SV has a nice easy simple adjuster. Try not to skin yer hands so get a extra bar on the c-spanner for the collar for extra purchase.