How many miles on the bike? The rear shock could need rebuilt/replaced. I agree the damping screws should not be fully turned one way or the other.
I used to chew through rear tires on the Multistrada in <2500 miles on a Gap trip. I was 1-up and running fully adjustable Ohlins front and rear. I can see how a heavy bike, 2-up with OEM spec suspension could burn through a tire in the same manner.
Personally, I would start with a high end shock set to factory suggested settings and see how it goes from there. Your pic doesn't look that bad in my opinion. It's been hot and you know how to ride. Tires have to compensate for inadequate suspension. This causes premature wear for sure.