Oh dear...
Seems there's a rash of them at the moment... I hope the bumps and bruises aren't too painful, and the bike's not too bad

The main question has to be why did the tyre break traction in the first place? There must have been something that caused it to let go. I suspect the answer to both your "oops" and the other one is trying to twist the throttle and accelerate whilst leant over...
Once it's gone however, why did things get out of hand? I think there's likely to be two parts:
1) You're looking at a big motor - loads of horsepower that'll overwhelm the rear tyre with no difficulty on a slippery surface. I've wheelspun a CG125 on a wet surface (on decent 125 tyres too before someone comments) with only 11hp available at peak revs on full throttle, and I've wheelspun a tuned 50 with probably 6hp tops on gravel. Forget the tyre width, it doesn't take much power for a bike to break traction even with a tyre adapted to the conditions if the surface isn't there.
2) once the rear starts to go, you're going to do all sorts of strange things with the clutch and throttle. It's such a routine operation, turning out of a side road onto a main road, that most people forget the necessity to lock onto the tank and keep a light grip on the bars.
The solution is not to try to power round the turn, but to go out straighter and a bit slower, turn tighter and get the bike pointed where you want to go next BEFORE twisting the throttle. Basically, it's a version of Point and Squirt, and once upright, wheelspin isn't a problem, and this technique really doesn't add anything to the time it takes to get out of the junction - if anything it's faster because once upright, you can put the power on as hard as you like, whilst you have to be much more careful for longer is you power on as you lean.
Some points about grip and traction.
First, the way friction works is that once traction is LOST, you have to have to reduce what you are asking for to well below the point at which you lost traction in the first place, for it to REGAIN grip.
Second, low revs tend to demand more throttle to get the same drive - take a look at "thrust curves", not just torque or hp. Thrust is a measure of how the power is put down by the gearbox and in lower gears you get more thrust at any particular revs. But petrol engines aren't equally efficient across the entire rev range, and most Japanese engines develop the power towards the top end, even ones "retuned for mid-range"!! The "bump" of the torque curve is up the rev range - to get the same thrust at lower revs (ie same speed in a higher gear), you need to feed more fuel into the motor to get a bigger bang.
Now, put those two points together - so long as the tyre's gripping, the bigger handful's not a problem, but if the tyre breaks loose on a slippery patch, you've now feeding a lot of fuel into a motor that is rapidly spinning up into its efficient zone - as the rear spins up, the motor starts producing MORE power even if you keep the throttle steady and virtually guarantees that the tyre won't grip again! This is why the advice to run a high gear on a slippery surface is out of date for modern sports bikes - it's designed for low and slow revving engines with relatively little power - think 60s BMWs and Triumphs. This is not just my thinking - it's what Ron Haslam teaches in the wet! At really slow speeds, you're down first at the bottom of the rev range, so slipping the clutch means that you get the revs up higher without going any faster, so you're less likely to get a sudden "spin up" response if the rear does break traction.
What else? You might find getting into second and slipping the clutch also helps - not having ridden an SV I can't say for sure - because it seems to take the edge off the throttle response. Make sure you are REALLY slipping the clutch too - you should be able to twist the throttle and the revs should surge but the bike shouldn't jerk forward, or back when you shut it again, so that if the rear did step out and you inadvertantly tweak the throttle you shouldn't make things worse! It's worth moving the clutch lever so you have more slack than the usual 1/2cm at the end of the lever if you do a lot of slow town work - it's easier to control it then particularly if you have small hands.
These are all tricks I've learned thru years of trial and error despatching in the worst weather, often on slippery and sometimes icy roads through the winter - it's not something that I've seen covered in any book on advanced riding.
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"Force has no place where there is need of skill" Herodotus 450BC :burnout: