Sadly no mater what you do, you are going to come out with non-optimal results. I would go with the oven method over the grill as you need to get the meat up, but you want to do it with out losing all the juice/fat you have already taken all the trouble to convert to gelatin. The grill is going to raise the outside of the meat much quicker that the inside (mostly, you can use your grill as an oven but in this case I don't think it brings anything to the table that you regular oven doesn't).
The best way, and by best, I mean the one with the tastiest results, is going to be put the butt in a 200 to 250 degree oven and let it come up to temp. This method is going to take the longest but will preserve the meat that come off the grill as close as you could.
Or, you can heat just like a roast and let the outside overcook a bit.
or, depending on how you are serving the finished product, you can slice cold and finish in a skillet to heat though... this would be great if you are doing sandwiches or pulled pork.
If you are feeling adventurous, 130 degrees plus smoke is a little on the rare side but it would still be delicious... not for this one as you let is cool on the counter top and fridged it but on the next one, I might just eat it then.
What can you do with pork fat?
Cook the bits over med-low heat to render out the fat. You can strain the rendered fat and use it as lard- make biscuits or pastry. Or you can get crafty and make soap or candles- but these are not within the scope of this site.
I had some Kazakhi friends in Russia who made a dish called "Плов" (Plov).
http://www.say7.info/cook/recipe/118-Plov.html
They would render pork fat this way and continue until the fatty bits were well fried. They would then scoop out the fried bits (and eat them) then fry onion and then carrot in the fat. Add some pork and fry until browned. Then add rice and water and a head of garlic on top, cover until the rice is done. Delicious.
Best Answer
It is difficult to predict when you will reach your foiling target, but the general rule of thumb for pulled pork at your stated cooking temperature is about 1.5 hours per pound, with some general allowances for margin of error.
I would plan on the entire cook taking about 5-6 hours, but be ready for it to be finished in 4. At about 3 hours, start checking temperatures to determine when you will want to foil your roast.
Final note: If your intent is to make pulled pork, do NOT assume that it is done just because it is at 190f. Your thermometer probe should slide in and out of the meat with virtually zero resistance.