Grilling to me means cooking a thinner piece of meat at direct high temps. Technically, cooking at 350 is roasting, but it doesn't seem to matter much. Looking at pictures of butts at 4 hours on smokers at 225 - 250 that have been posted here, the butts that I've done at 350 (indirect of course) look virtually the same at that point. And when they're finished at a lower temperature, they end up the same as Q that I've eaten using the 250 and no more method. It's still low and slow for the last half and the cook time isn't all that much different. I think the key is putting the butt on right out of a 37 degree 'fridge.
Like I say, it's not so much about speeding things up but not freaking out if the temps climb over 250. I think people put too much stock on keeping the temp at a constant lower temp. It's not a problem if you're using an electric smoker that can keep a constant temp but when you're using charcoal or wood, it can make life a lot easier knowing that you don't have to waste a lot of time and fuel trying to keep the temp at some arbitrary low temp. Heck, if you really want to go low and slow, as I said, you can actually go 170 for 8 hours after you've hit the butt with high temps. The butt has so much mass, you're not going to "overcook" it anytime soon, especially if the core temp is 37 degrees. And I've found that the outside doesn't overcook either.
But kudos for anyone that wants to keep it at 225 or 250. Fire management can be a big part of the fun. The thing is, it's just not necessarily necessary (if you catch my drift). When you use a
Weber kettle, it's a lot of fuss over nothing because the temps will only hold steady for about an hour - then you've got to refresh the coals and open the hood and lose a lot of the heat that you already have. Plus, when you refresh the coals, I find that if you put the lid back on, even a small amount of new coals will kick the temps up to 300+. Then you've got to fiddle with the lid and all that. Too much drama when it's not really necessary.
For those who have nice big Lang rigs or any other larger unit, it's probably easier to keep a constant temp, so those folks don't need to worry about it. But for those of us who have smaller units, I say, hit it with whatever heat you've got for 4 hours because I've found that it doesn't really make any difference. Of course, it only stays at 350 for an hour and then it starts to drop. I usually don't refresh the coals until it hits between 200 - 225 so it's not llike I'm cooking at 350 the whole time. But at least I don't have to remove the lid or peek or anything. I only have to open it twice so it gets the full effect of the smoking.
Sorry for being typically too wordy...