A couple of hours should do it on the fatty - pull when it reaches internal 165. Foil. Set for a while. Slice. Enjoy.
I don't know how many people will be eating the fatty, but I NEVER cook only one. You'll be surprised how well they go over. Of course, if that's all you have, you just have to be careful you reach for a piece and pull back a nub :)
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And now, brethren, I commend you to God, and to the word of his grace, which is able to build you up, and to give you an inheritance among all them which are sanctified. [Acts 20:32 KJV]