I guess I am the oddball here but I have ALWAYS smoked butts and briskets fat side down, facing the heat source. I've done this on Kamados, my #3 as well as offsets that I've had where the heat source comes from the side but below and on my KBQ. So I don't think that's the issue. There is a LOT of fat inside the butt, the fat cap is not what makes the butt moist, it's like an old wives tale that keeps getting perpetuated and argued about on BBQ forums the world over and it will continue to be that way, lol. My take on having the fat cap act as a way to "baste" the meat only serves as a way to wash off rub and weaken your bark. As a matter of fact, I've trimmed the whole dang thing off and cooked one and it gave me more bark on all sides. I usually don't bother with that though and I have never ever scored a fat cap.
So what do I think you could do to better your results? Use a small mini loaf pan full of water placed next to your smokebox and buy a better butt. Crazy I know, but all butts are not the same. The SI is a fantastic smoker but it can't work miracles with poor meat. You get out of it what you put into it. I have bought butts from Costco, Sams, Restaurant Depot, Kroger, Publix, Food Depot (local little crappity stores in the South) and Wal-Mart. The best ones I have found are actually Smithfield butts from Wally World/Sams. They are nicely marbled and come PRE INJECTED (brined) with a sodium solution. So while it sits in its cryovac waiting for you to buy it, its getting marinated/brined and it ALWAYS comes out tender and juicy. I have never cooked a bad Smithfield butt. The butts from Kroger and RD are fine but definitely NEED to be brined in Tony's brine to come out good. You did brine it so we can't blame the brine. We can't blame the smoker because we know what it can do. What can we blame? The meat.
Food Depot butts are absolutely terrible. If I were to use it in a dish that hid it, I would use one in a pinch but I'd buy one at Kroger or Publix before I'd stoop that low again and to be quite honest, Publix butts are TOO high and not all that great either. Wal-Mart is my go to for butts as well as ribs. I am a big fan of Smithfield products. If they win Moe Cason awards then they're good enough for me!
I am by no means a know it all. More like a know nothing but that's my experience for what it's worth. I have faith that the SI will redeem itself and that you'll be singing its praises soon