The longest, predictably, was Dallas to Sydney, which clocked in at 16:58. There were a number of others, (Sydney-Dubai) that were in the 16:45 region, though I expect they had appreciable holding. It's not just flight time that you need to consider, but duty period. Even back on the 747, I hit 20 hours a couple of times, when things had gone wrong at the departure end, or we'd had to divert.
How tired you are isn't a direct function of the flight's length. I'm sure that some of AV's domestic days leave him pretty shattered, I know that the 767 domestic operation could be more tiring than international. Early starts, no real chance to get a break. Day after day.
With regard to the ULR ops, much will depend upon the quality of the crew rest provisions. I expect that they'll go with the cheapest possible option, and that means that there's unlikely to be the sort of setup that the 380 has. No matter what is there, it's likely that on many occasions the crew (or individuals with the crew) will be arriving in an extremely tired state.