I'd say you're chasing at least 2 issues here, it's important to look at each symptom, and check they are linked.
1) It's cold at the moment, in cold weather the battery's got less go, the oil is thicker and a bigger ask is being made to turn the bike over, so check the connections to the battery, the main earth, the starter solenoid and the starter motor itself are clean (take them apart, use a brass brush) and use a little oil or grease on them to help keep them that way. Rubbish electrical connections won't help the battery turn the motor any.
2) Check the choke plungers aren't stuck, water gets down the choke cable to a Y-piece splitter to the left of the engine, runs down to the choke plungers (usually the front carb) and sticks them on. The fueling is now rubbish. A sooty plug on one or both cylinders can be a symptom of this. It's well documented, take the plungers out, clean them up, oil the cable and pack the Y-pice full of grease.
3) When you're doing fast A road miles in cold temperatures, with high humidity, you're in perfect conditions for carb-icing. Yes the SV has carb heaters, but they're a bit pants (like most carb heaters). Use a fuel additive such as Silkoline Pro FST, or try using a Super unleaded like Shell V-Power or BP Ultimate. Makes a difference to carb icing but won't get you any more power
HTH
Jambo