I may get disagreement on this, but if you're confident about getting to the top that quickly, you could go without jacket and gloves. My Ascent times are around 3:30, and as long as the forecast looks good the night before, I go in shorts and t-shirt only, and put my warm stuff in the sweat check bag.
Having said that, are you confident that you'll be up that quickly? Are you used to elevation? Are you familiar with Barr Trail? If not, many people every year expect to run a certain time and then end up taking way longer in the cold above treeline than expected.
As for your other question, just bring loose items for the sweat check bag, don't bring a pre-packed backpack, as it may not fit in the bag. The bags are a good size, but it's a lot easier to squash individual items into them.