Joe: This might be of interest. I think it is actually closer to 6 miles each way on the MR. When I was on the MR on 8/8 & 8/9 I took along my Garmin 405 running watch just for kicks. If you are not familiar with the Garmin 405, they are pretty slick and I believe very accurate. If you run a certified 10K course or whatever the mileage is right on.
According to my Garmin it was 3.40 miles from the trailhead to UBSL, and 3,186' of elevation gain. This would likely include me getting slightly off route once and going too high.
From UBSL to Iceberg Lake the Garmin showed 1.63 miles and 1,315' of elevation gain. The hiking time is off as I left it running during some of the water breaks and also left it running while I was walking around for several minutes at Iceberg Lake, so it will be a little less than 1.63 miles.
The Garmin shows the total as 5.03 miles from the TH to Iceberg Lake and 4,501' feet of elevation gain. Unfortunately my watch battery died at Iceberg Lake, so I didn't record any data up the gully. The watch battery is made to get you through a marathon, but apparently not for a two day hike. Obviously we know it is approximately another 1,874' from Iceberg Lake to the summit. The Garmin seems very accurate on the road, but who knows in this application. I do not claim this to be any more accurate than other measurements others may have done. Take it for what it is worth. If for some strange reason anybody has a burning curiosity I can e-mail a link to the downloaded data from the watch.