[yokohama]

The rear Battlax S20 was gone at just under 3,500 on my XSR900 and I don't ride like a hooligan either.
What pressures are you running? I think Yamaha recommend 36 & 42 and that's on a bike which doesn't weigh much more than the SV. Reducing the pressure might help a little.

I chose the XSR900 over the MT09 as i preferred the looks and it was supposed to have better suspension, a less snatchy throttle response and improved fuelling map. Throttle response is mostly smooth but I have very similar suspension issues to you.
I'd read on some forums that the suspension was firm and I'm only around 65kg so when I picked it up, I asked the dealer to soften the rear preload a couple of notches for me. They refused saying they preferred the customer to ride it on factory settings first and then decide, which I took to be doublespeak for liability avoidance should any mishap occur. Anyway, I rode it home steadily in the pouring rain and on A roads. It was fine.
A couple of days later I took it out on in the Dales on some B roads and was pottering along when there was a huge bang and I was lifted a few inches out of the saddle, both feet came off the pegs and i retrospect, probably quite fortunate not to come off. I'd hit my first bump, pothole or whatever and as I continued, the firmness of the suspension became much more noticeable.
Once I got home, I found both tyres were over the recommended pressures so changed those, backed off the rear preload to minimum, softened the rebound and it's improved but still too firm. Any bump and I get a serious kick up the butt.
The front is slightly better. Preload is reduced (I haven't played with the rebound yet) and I can just about live with it but the rear is possibly too stiff for my weight, does spoil the experience and is becoming increasingly irritating.
There's a suspension guy in Leeds who seems to have a good rep for setting bikes up so I'm thinking of trying him before I look at more serious investment. Otherwise it might have to be a new rear shock. There's lots of suspension talk on FZ09.org forum. Most guys on there seem to put Andreani kits in the front and Nitron/Ohlins units on the rear.

I thought I'd let you know you're not alone but having paid extra for a bike with supposedly upgraded and adjustable suspension, I can understand your frustration. Hindsight is a wonderful thing but it might have been better to buy the standard MT09 and then let Reactive upgrade the suspension with springs and settings specifically suited to your weight.