The 6550's will NOT work with the 13S.
I've had one for about 2-1/2 years now. I've used the stock tubes, EH EL34B's and the Gold Lion KT77's. I went all Gold Lion reissues for the small tubes as well.
I can absolutely say the Gold Lion KT77's are, imo, the best power tubes I've used, with the caveat that they tend to be a bit more floaty in the bias than the stock blue bottles. So it's something to keep an eye on, if you end up checking them out.
I honestly didn't like the 1st quad of them I got. They sounded "weird" to me. Sold I sold them, which happened quick because of their reputation. About a year later I figured maybe there might be something to them if so many people seemed to like them, and I got another quad, figuring if I still didn't like them, after 50 hours, I could sell them pretty easily. After that I fell in love with them.