The new PR2 I recently mounted on my bike came with 7/32" of tread in the rear tire. The inside edge of the lettering on a quarter is about 3/32", which is what it appears from your picture you have left. The PR2 I removed had just hit zero tread depth at a little over 9500 miles. If this was my rear tire I would be able to get 3 / 7 * 9500 = 4,070 miles out of that tire. So I would have no hesitation to take it on a 2k mile trip.
But, I would have already clocked off ~ 5400 miles to get to that point of wear. If you have only ridden 2700 miles to get there then your remaining miles should be half of mine. Which was why Wheaton asked the questions he did. If you never track your mileage you'll never know what you have left.
PS - the last two guys weren't kidding. They really do run those tires on their bikes. I (obviously) am running Michelin PR2's.