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.
I have "ice packs" which are encased in plastic (some hard, some soft), that I keep frozen. It won't quite bring your soup down as far as you want, but dropping a few of these into your soup will help cool it off. Just remember to clean them before returning them to the freezer.
The other thing I do it put the stopper in my sink and add cold water and ice. The whole pot goes in the sink--surrounded by cold water and ice it will cool much faster than in the fridge (or freezer). Add some salt to the ice-water and it will get even colder. Stir it up a bit every once in a while both inside and outside (use separate spoons!) to keep the temperature distribution even.
Alternatively, you could use one of these :)
Best Answer
I agree with the comment by Richard ten Brink: you can't really do this in a home freezer and expect good results. Even with a large home chest freezer, it will take way too long for a whole carcass to freeze all the way through. Freezing requires a lot more energy than maintaining something that's already frozen, and the process for a pig carcass would probably take several days (depending on the size of the pig). You'd likely get significant quality degradation during the freezing process itself: slower freezing means more damage to cells, which affects meat quality when defrosted, not to mention that it could take many days for the interior to freeze solid (which could also impact quality).
And "freezer burn," by the way, isn't necessarily caused by long storage: it's the result of poor packing, usually combined with temperature cycling in a freezer, which allows air near the surface of food to lead to oxidation and dehydration. Yes, a poorly packaged food will get worse over time, but a properly packaged food will last years in the freezer with no freezer burn. (For a whole hog, you'll need a large chest freezer at home, preferably one without an auto-defrost cycle.)
Anyhow, my personal recommendation would be to seek out a local meat packer or meat processor with access to a commercial freezer. (Perhaps there's someone who people take game meat to for processing or something?) Ask them if they'd be willing to freeze the carcass after slaughter and vacuum seal it for you. The vacuum sealing will significantly help to prevent freezer burn. I don't know whether vacuum packing is feasible depending on how large the pig is (many processors only do it with small whole pigs), but that would be your best bet.
They'd also be able to advise you on the feasibility of freezing a larger pig for that long if they can't vacuum seal it. But my guess is that it should be fine for a few months if you can keep it consistently below 0F and away from temperature cycling.