Slow Cooking a Whole NY Strip

I have a Big Steel Keg, (similar to the Green Egg), and have done a lot of slow cooking pork, turkeys, etc. I have a whole, untrimmed NY Strip, about 12#. Typically I would cut into steaks, or could probably cook it like a conventional roast, at 350-400 until it reaches 135. But, I would like to slow-cook it, with some charcoal/smoke. I have a temp control on the Keg, can maintain a consistent heat. My thoughts were cook it in a pan, do not trim too much of the fat pad, maybe 195 degrees for several hours, checking the internal temp. Letting it rest for a good long time before eating. Anyone ever done anything like this? Appreciate any thoughts, Thanks

Slow Cooking a Whole NY Strip